Team Worker. Creative Thinker. Effective Participator. Independent Enquirer. Reflective Learner. Self Manager. Real life cross/curricular links?. Where are we in our journey?. Which ones are you using?. PLT Skills. LESSON OBJECTIVES. Always aim high!. We are learning to:
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Creative Thinker
Effective Participator
Independent Enquirer
Reflective Learner
Self Manager
Real life cross/curricular links?
Where are we in our journey?
Which ones are you using?PLT Skills
LESSON OBJECTIVES
Always aim high!
We are learning to:
AUTHOR
www.mistrymaths.co.uk
BRAIN IN GEAR
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EXAMPLE
DITDIONA can be rearranged to make ADDITION
TASK
Work out the following Mathematical anagrams:
Cyclic
Symmetry
Quadrant
EXTENSION
Develop your own Mathematical anagrams as above as a creative thinker.
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STARTER
PLT Skills
TASK
Work out x:
Find the area of:
Write 8600000 in standard form
1)
3)
2)
3x + 6
4x  5
7cm
x + 11
2x + 8
6cm
6
8.6
x 10
5cm
=
7
8 x 5
4x  5
x + 11
2x + 8
= 360
3x + 6
+
+
+
=
8cm
10
2
= 360
10x
+ 20
 20
10x
 20
= 340°
3
2
25
÷ 10
÷ 10
EXTENSION
x = 34°
Work out x:
Value of:
4)
5)
x
Power

Reciprocal
120°
7m
Root
4m
110°
Pentagon adds to 540°
1
118°
8m
=
93°
5m
3
)
(
25
9
9
1
1
x
=
x
=
3
4
8
4
125
5
Work out x:
x
=
540°
 93°
 110°
 120°
 118°
x
=
8
x
=
x
=
99°
x
=
18m
Area of a triangle =
9m
4m
2
Area of a triangle = 20cm
x
8m
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TRIGONOMETRIC ANGLES
INTRODUCTION – SINE CURVE
sin x is negative in the third quadrant
sin x is negative in the fourth quadrant
sin x is positive in the second quadrant
sin x is positive in the first quadrant
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TRIGONOMETRIC ANGLES
INTRODUCTION – COSINE CURVE
cos x is negative in the second quadrant
cos x is negative in the third quadrant
cos x is positive in the fourth quadrant
cos x is positive in the first quadrant
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TRIGONOMETRIC ANGLES
INTRODUCTION – TANGENT CURVE
tan x is negative in the second quadrant
tan x is negative in the fourth quadrant
tan x is positive in the first quadrant
tan x is positive in the third quadrant
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TRIGONOMETRIC ANGLES
SINE CURVE – TRIGONOMETRIC ANGLES
For which angles does sin x = 0.5?
30° and 150°
150°
30°
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TRIGONOMETRIC ANGLES
SINE CURVE – TRIGONOMETRIC ANGLES
For which angles does sin x = 0.5?
210° and 330°
210°
330°
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TRIGONOMETRIC ANGLES
COSINE CURVE – TRIGONOMETRIC ANGLES
For which angles does cos x = 0.5?
60° and 300°
60°
300°
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TRIGONOMETRIC ANGLES
COSINE CURVE – TRIGONOMETRIC ANGLES
For which angles does cos x = 0.5?
120° and 240°
120°
240°
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TRIGONOMETRIC ANGLES
TANGENT CURVE – TRIGONOMETRIC ANGLES
For which angles does tan x = 1?
45° and 225°
225°
45°
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TRIGONOMETRIC ANGLES
TANGENT CURVE – TRIGONOMETRIC ANGLES
For which angles does tan x = 1?
45° and 135°
45°
135°
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TRIGONOMETRIC CURVES
Cyclic → Repeat their pattern indefinitely in both directions
Every value of sine between 1 and 1 gives two angles between 0° and 360°
When the value of sine is positive, both angles are between 0° and 180°
When the value of sine is negative, both angles are between 0° and 180°
Cyclic → Repeat their pattern indefinitely in both directions
Every value of cosine between 1 and 1 gives two angles between 0° and 360°
When the value of cosine is positive, one angle is between 0° and 90° and the other is between 270° and 360°
When the value of cosine is negative, both angles are between 90° and 270°
Every value of tangent between 1 and 1 gives two angles between 0° and 360°
When the value of tangent is positive, one angle is between 0° and 90° and the other is between 180° and 270°
When the value of tangent is negative, one angle is between 90° and 0° and the other is between 90° and 180°
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CAST DIAGRAM
90°
Sin (+)
All (+)
Onlysin θ
is positive in this quadrant
All of sin θ, cos θ
and tan θ are positive in this quadrant
Quadrant 1
Quadrant 2
0°
180°
/
360°
Tan (+)
Cos (+)
Onlycos θ
is positive in this quadrant
Onlytan θ
is positive in this quadrant
Quadrant 3
Quadrant 4
270°
CAST
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TRIGONOMETRIC ANGLES
cos 330°
tan 210°
sin 150°
cos 30° = …………….
tan 30° = …………….
sin 30° = …………….
cos 210°
tan 330°
sin 330°
cos 150° = …………….
tan 150° = …………….
sin 210° = …………….
90°
Sin (+)
All (+)
150°
30°
Onlysin θ
is positive in this quadrant
All of sin θ, cosθ
and tan θ are positive in this quadrant
sin θ
sin θ
y
y
180°
0°
/
360°
cosθ
cosθ
sin θ
sin θ
y
x
y
x
Tan (+)
Cos (+)
210°
330°
Onlycosθ
is positive in this quadrant
Onlytan θ
is positive in this quadrant
270°
CAST
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TRIGONOMETRIC ANGLES
EXAMPLES – SIN θ
1)
2)
Find the other angle which has the same value as sin 225°
Find the other angle which has the same value as sin 60°
sin 120°
sin 315°
120°
60°
225°
315°
Reflection in the yaxis
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EXAMPLES – COS θ
1)
2)
Find the other angle which has the same value as cos 225°
Find the other angle which has the same value as cos 60°
cos 300°
cos 135°
60°
135°
225°
300°
Reflection in the xaxis
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EXAMPLES – TAN θ
1)
2)
Find the other angle which has the same value as tan 225°
Find the other angle which has the same value as tan 60°
tan 240°
tan 315°
60°
135°
315°
240°
Makes a diagonal line
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TASK 1 (GRADE A*) – SIN θ
1)
Find the other angle which has the same value for the following:
sin 135°
(a)
sin 100°
sin 155°
sin 45°
(c)
(b)
sin 25°
sin 80°
100°
80°
135°
45°
155°
25°
sin 20°
sin 260°
(d)
sin 350°
sin 160°
(f)
(e)
sin 280°
sin 190°
20°
160°
190°
350°
280°
260°
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TASK 2 (GRADE A*) – COS θ
1)
Find the other angle which has the same value for the following:
cos 315°
(a)
cos 280°
cos 335°
cos 45°
(c)
(b)
cos 25°
cos 80°
80°
45°
25°
315°
335°
280°
cos 200°
cos 100°
(d)
cos 170°
cos 160°
(f)
(e)
cos 260°
cos 190°
100°
160°
170°
190°
200°
260°
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TASK 3 (GRADE A*) – TAN θ
1)
Find the other angle which has the same value for the following:
tan 225°
(a)
tan 260°
tan 205°
tan 45°
(c)
(b)
tan 25°
tan 80°
80°
45°
25°
225°
205°
260°
tan 340°
tan 100°
(d)
tan 10°
tan 160°
(f)
(e)
tan 280°
tan 190°
100°
160°
10°
190°
340°
280°
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TASK 4 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ
1)
Find the other angle which has the same value for the following:
sin 145°
tan 235°
(a)
cos 295°
sin 35°
(c)
(b)
tan 55°
cos 65°
65°
55°
35°
145°
235°
295°
cos 255°
tan 255°
sin 345°
(d)
cos 75°
(f)
(e)
sin 15°
tan 75°
75°
75°
165°
15°
255°
255°
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TASK 4 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ
2)
Find the other angle which has the same value for the following:
sin 65°
cos 235°
(a)
tan 320°
sin 115°
(c)
(b)
tan 140°
cos 125°
115°
65°
125°
140°
320°
235°
cos 195°
sin 50°
(d)
tan 355°
cos 165°
(f)
(e)
sin 130°
tan 175°
130°
50°
165°
175°
355°
195°
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TASK 4 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ
3)
Find the other angle which has the same value for the following:
sin 340°
(a)
cos 100°
tan 85°
sin 200°
(c)
(b)
tan 265°
cos 260°
100°
85°c
340°
200°
260°
265°
cos 165°
sin 325°
(d)
tan 5°
cos 195°
(f)
(e)
sin 215°
tan 185°
165°
5°
185°
195°
325°
215°
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TASK 4 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ
4)
Find the other angle which has the same value for the following:
sin 250°
(a)
cos 80°
tan 170°
sin 290°
(c)
(b)
tan 350°
cos 280°
80°
170°
350°
290°
250°
280°
cos 65°
sin 195°
(d)
tan 130°
cos 295°
(f)
(e)
sin 345°
tan 310°
65°
130°
345°
195°
310°
295°
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TRIGONOMETRIC ANGLES
EXTENSION 1 (GRADE A*) – WITHOUT A CAST DIAGRAM
1)
Find the other angle which has the same value for the following:
sin 130°
(a)
cos 320°
tan 260°
sin 50°
(c)
(b)
tan 80°
cos 40°
cos 230°
(c)
tan 350°
sin 60°
cos 130°
(e)
(d)
sin 120°
tan 170°
tan 235°
(f)
sin 55°
cos 175°
tan 55°
(h)
(g)
cos 185°
sin 125°
sin 260°
(i)
tan 350°
sin 105°
sin 280°
(k)
(j)
sin 75°
tan 170°
sin 132°
(l)
cos 291°
tan 199°
sin 48°
(n)
(m)
tan 19°
cos 69°
cos 143°
(o)
tan 104°
sin 44°
cos 217°
(q)
(p)
sin 136°
tan 284°
tan 132°
(r)
cos 181°
sin 168°
tan 312°
(t)
(s)
sin 12°
cos 179°
sin 181°
(u)
cos 245°
tan 23°
sin 359°
(w)
(v)
tan 203°
cos 115°
cos 59°
(x)
tan 21°
sin 179°
cos 301°
(z)
(y)
sin 1°
tan 201°
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TRIGONOMETRIC ANGLES
EXAMPLES 2 – SIN θ
1)
2)
Find the angles with a sine of 0.256
Find the angles with a sine of 0.52
1
sin
0.52 =
31.3°
1
sin
0.236 =
14.8°
31.3° and 148.7°
194.8° and 345.2°
148.7°
31.3°
194.8°
345.2°
Reflection in the yaxis
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EXAMPLES 2 – COS θ
1)
2)
Find the angles with a cosine of 0.372
Find the angles with a cosine of 0.68
1
cos
0.68 =
47.2°
1
cos
0.372 =
111.8°
47.2° and 312.8°
111.8° and 248.2°
111.8°
47.2°
312.8°
248.2°
Reflection in the xaxis
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EXAMPLES 2 – TAN θ
1)
2)
Find the angles with a tangent of 1.2
Find the angles with a tangent of 0.715
1
tan
0.715 =
35.6°
1
tan
1.2 =
50.2°
35.6° and 215.6°
129.8° and 309.8°
129.8°
35.6°
215.6°
309.8°
Makes a diagonal line
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TASK 5 (GRADE A*) – SIN θ
1)
State the two angles between 0° and 360° for each of these sine values:
1
(a)
sin
0.2
0.2 =
11.5°
(c)
(b)
1
0.5
1
0.7
sin
sin
0.7 =
0.5 =
44.4°
30°
44.4°
135.6°
150°
30°
11.5°
168.5°
11.5° and 168.5°
44.4° and 135.6°
30° and 150°
(d)
1
0.4
sin
0.4 =
23.6°
(f)
1
1
(e)
sin
sin
33.4°
0.136
0.55
0.55 =
0.136 =
7.8°
187.8°
352.2°
203.6°
213.4°
336.4°
326.6°
203.6° and 336.4°
213.4° and 326.6°
187.8° and 352.2°
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TASK 6 (GRADE A*) – COS θ
1)
State the two angles between 0° and 360° for each of these cosine values:
1
(a)
cos
0.4
0.4 =
66.4°
(c)
(b)
1
0.5
1
0.6
53.1°
cos
cos
0.6 =
0.5 =
60°
66.4°
60°
53.1°
293.6°
300°
306.9°
66.4° and 293.6°
53.1° and 306.9°
60° and 300°
(d)
1
0.1
cos
0.1 =
95.7°
(f)
1
1
(e)
cos
cos
130.5°
0.241
0.65
0.65 =
0.241 =
103.9°
95.7°
103.9°
130.5°
229.5°
256.1°
264.3°
95.7° and 264.3°
130.5° and 229.5°
103.9° and 256.1°
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TASK 7 (GRADE A*) – TAN θ
1)
State the two angles between 0° and 360° for each of these tangent values:
1
(a)
tan
0.8
0.8 =
38.7°
(c)
(b)
1
0.3
1
0.1
5.7°
tan
tan
0.1 =
0.3 =
16.7°
38.7°
16.7°
5.7°
185.7°
196.7°
218.7°
38.7° and 218.7°
5.7° and 185.7°
16.7° and 196.7°
(d)
1
0.9
tan
0.9 =
42.0°
(f)
1
1
(e)
tan
tan
19.3°
0.682
0.35
0.35 =
0.682 =
34.3°
138°
145.7°
160.7°
340.7°
318°
325.7°
138° and 318°
160.7° and 340.7°
145.7° and 325.7°
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TASK 8 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ
1)
State the two angles between 0° and 360° for each of these values:
1
tan
0.5 =
26.6°
1
cos
0.8 =
36.9°
1
(a)
sin
sine of 0.1
0.1 =
5.7°
(c)
(b)
tangent of 0.5
cosine of 0.8
36.9°
26.6°
174.3°
5.7°
206.6°
323.1°
5.7° and 174.3°
26.6° and 206.6°
36.9° and 323.1°
1
(d)
cos
0.6 =
cosine of 0.6
53.1°
(f)
(e)
sine of 0.9
tangent of 0.4
1
sin
0.9 =
64.2°
1
tan
0.4 =
21.8°
115.8°
64.2°
53.1°
21.8°
201.8°
306.9°
53.1° and 306.9°
64.2° and 115.8°
21.8° and 201.8°
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TASK 8 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ
2)
State the two angles between 0° and 360° for each of these values:
1
tan
0.12 =
6.8°
1
cos
0.62 =
51.7°
1
(a)
sin
sine of 0.27
0.27 =
15.7°
(c)
(b)
tangent of 0.12
cosine of 0.62
51.7°
164.3°
15.7°
6.8°
186.8°
308.3°
15.7° and 164.3°
6.8° and 186.8°
51.7° and 308.3°
(d)
Cosine of 0.86
(f)
(e)
sine of 0.38
tangent of 0.75
1
cos
0.86 =
30.7°
1
sin
1
0.38 =
tan
22.3°
0.75 =
36.9°
30.7°
36.9°
157.7°
22.3°
216.9°
329.3°
30.7° and 329.3°
22.3° and 157.7°
36.9° and 216.9°
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TASK 8 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ
3)
State the two angles between 0° and 360° for each of these values:
1
tan
0.8 =
38.7°
1
cos
0.5 =
120°
1
(a)
sin
sine of 0.3
0.3 =
17.5°
(c)
(b)
tangent of 0.8
cosine of 0.5
120°
141.3°
342.5°
197.5°
321.3°
240°
197.5° and 342.5°
141.3° and 321.3°
120° and 240°
(d)
cosine of 0.6
(f)
(e)
sine of 0.4
tangent of 0.2
1
cos
1
0.6 =
sin
1
126.9°
0.4 =
tan
23.6°
0.2 =
11.3°
126.9°
168.7°
348.7°
203.6°
336.4°
233.1°
126.9° and 233.1°
203.6° and 336.4°
168.7° and 348.7°
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TASK 8 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ
4)
State the two angles between 0° and 360° for each of these values:
1
tan
0.69 =
34.6°
1
cos
0.62 =
128.3°
1
(a)
sin
sine of 0.46
0.46 =
27.4°
(c)
(b)
tangent of 0.69
cosine of 0.62
128.3°
145.4°
152.6°
27.4°
325.4°
231.7°
27.4° and 152.6°
145.4° and 325.4°
128.3° and 231.7°
(d)
cosine of 0.24
(f)
(e)
sine of 0.84
tangent of 0.48
1
cos
0.24 =
103.9°
1
tan
1
0.48 =
25.6°
sin
0.84 =
57.1°
103.9°
154.4°
334.4°
256.1°
237.1°
302.9°
103.9° and 256.1°
237.1° and 302.9°
154.4° and 334.4°
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EXTENSION 2 (GRADE A*) – WITHOUT A CAST DIAGRAM
1)
State the two angles between 0° and 360° for each of these values:
(a)
sine of 0.5
30° & 150°
(c)
(b)
tangent of 0.7
cosine of 0.2
78.5° & 281.5°
35° & 215°
(d)
cosine of 0.8
36.9° & 323.1°
(f)
(e)
sine of 0.1
tangent of 0.5
26.6° & 206.6°
5.7° & 174.3°
6.8° & 186.8°
24.5° & 335.5°
(g)
tangent of 0.12
(i)
(h)
cosine of 0.91
sine of 0.83
56.1° & 123.9°
12.4° & 192.4°
(j)
sine of 0.47
28° & 152°
(l)
(k)
sine of 0.72
46.1° & 133.9°
tangent of 0.22
47.7° & 312.3°
39.9° & 219.9°
(m)
sine of 0.462
27.5° & 152.5°
(o)
(n)
tangent of 0.836
cosine of 0.673
158.2° & 338.2°
126.9° & 233.1°
(p)
cosine of 0.6
(r)
(q)
sine of 0.8
tangent of 0.4
233.1° & 306.9°
163.3° & 343.3°
154.2° & 205.8°
(s)
tangent of 0.3
(u)
(t)
sine of 0.5
cosine of 0.9
210° & 330°
105.1° & 254.9°
136.8° & 316.8°
(v)
sine of 0.63
219.1° & 320.9°
(x)
(w)
tangent of 0.94
cosine of 0.26
154.8° & 334.8°
224.4° & 315.6°
97.5° & 262.5°
(y)
cosine of 0.13
($)
(z)
sine of 0.71
tangent of 0.47
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MINIPLENARY 1 – ASSESSING UNDERSTANDING
A student has been struggling with trigonometric angles. Her answers are shown below. What is she doing wrong and how would you help her?
QUESTION
Find the other angle which has the same value for the following:
sin 335°
(a)
cos 118°
tan 230°
sin 25°
(c)
(b)
tan 50°
cos 62°
118°
62°
50°
155°
25°
335°
230°
220°
298°
cos 298°
sin 155°
cos 230°
(Reflection in xaxis)
(Reflection in yaxis)
(Diagonal line)
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TRIGONOMETRIC ANGLES
MINIPLENARY 2 – ASSESSING UNDERSTANDING
A student has been struggling with trigonometric angles. Her answers are shown below. What is she doing wrong and how would you help her?
QUESTION
State the two angles between 0° and 360° for each of these values:
(b)
(a)
(a)
cosine of 0.32
sine of 0.8
(c)
(c)
tangent of 0.2
71.3°
1
1
cos
sin
53.1°
0.32 =
0.8 =
1
tan
11.3°
0.2 =
198.7°
53.1°
126.9°
71.3°
168.7°
11.3°
191.3°
348.7°
306.9°
288.7°
53.1° & 126.9°
168.7° & 348.7°
71.3° & 288.7°
(Reflection in yaxis)
(Reflection in xaxis)
(Diagonal line)
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What grade are we working at?
DISCOVERY
PLT Skills
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PLENARY ACTIVITY– PROBLEM SOLVING (GRADE A*)
Suppose the sine key on your calculator is broken, but not the cosine key. Show how you could calculate these:
(a)
sin 35°
cos 55°
cos 60°
(b)
sin 150°
90°  35° =
55°
90°  30° =
60°
55°
60°
35°
sin θ
150°
30°
sin θ
cosθ
cosθ
Need to make cosθ the same length as sin θ
Need to make cosθ the same length as sin θ
Where are we in our journey?
What have you learnt?
Draw your brain
In your brain, write or draw everything you can remember about finding trigonometric ratios of angles between 0°to 360. It can be a skill or a reflection, or something else that might be prominent in your brain.
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Enterprise Skills
Which ones are you using?
Plenary Activity
How well do you understand the task?
.
I fully understand
I don’t understand
I nearly understand
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WWW (What Went Well)
EBI (Even Better If)
On your post it notes…
Think about how you can improve your work.
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TRIGONOMETRIC ANGLES
TASK 1 (GRADE A*) – SIN θ
1)
Find the other angle which has the same value for the following:
(a)
sin 45°
(c)
(b)
sin 25°
sin 80°
(d)
sin 160°
(f)
(e)
sin 280°
sin 190°
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TASK 2 (GRADE A*) – COS θ
1)
Find the other angle which has the same value for the following:
(a)
cos 45°
(c)
(b)
cos 25°
cos 80°
(d)
cos 160°
(f)
(e)
cos 260°
cos 190°
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TASK 3 (GRADE A*) – TAN θ
1)
Find the other angle which has the same value for the following:
(a)
tan 45°
(c)
(b)
tan 25°
tan 80°
(d)
tan 160°
(f)
(e)
tan 280°
tan 190°
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TASK 4 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ
1)
Find the other angle which has the same value for the following:
(a)
sin 35°
(c)
(b)
tan 55°
cos 65°
(d)
cos 75°
(f)
(e)
sin 15°
tan 75°
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TASK 4 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ
2)
Find the other angle which has the same value for the following:
(a)
sin 115°
(c)
(b)
tan 140°
cos 125°
(d)
cos 165°
(f)
(e)
sin 130°
tan 175°
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TASK 4 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ
3)
Find the other angle which has the same value for the following:
(a)
sin 200°
(c)
(b)
tan 265°
cos 260°
(d)
cos 195°
(f)
(e)
sin 215°
tan 185°
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TASK 4 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ
4)
Find the other angle which has the same value for the following:
(a)
sin 290°
(c)
(b)
tan 350°
cos 280°
(d)
cos 295°
(f)
(e)
sin 345°
tan 310°
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EXTENSION 1 (GRADE A*) – WITHOUT A CAST DIAGRAM
1)
Find the other angle which has the same value for the following:
(a)
sin 50°
(c)
(b)
tan 80°
cos 40°
(c)
cos 130°
(e)
(d)
sin 120°
tan 170°
(f)
tan 55°
(h)
(g)
cos 185°
sin 125°
(i)
sin 280°
(k)
(j)
sin 75°
tan 170°
(l)
sin 48°
(n)
(m)
tan 19°
cos 69°
(o)
cos 217°
(q)
(p)
sin 136°
tan 284°
(r)
tan 312°
(t)
(s)
sin 12°
cos 179°
(u)
sin 359°
(w)
(v)
tan 203°
cos 115°
(x)
cos 301°
(z)
(y)
sin 1°
tan 201°
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TASK 5 (GRADE A*) – SIN θ
1)
State the two angles between 0° and 360° for each of these sine values:
1
(a)
0.2
(c)
(b)
0.5
0.7
(d)
0.4
(f)
(e)
0.136
0.55
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TASK 6 (GRADE A*) – COS θ
1)
State the two angles between 0° and 360° for each of these cosine values:
(a)
0.4
(c)
(b)
0.5
0.6
(d)
0.1
(f)
(e)
0.241
0.65
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TASK 7 (GRADE A*) – TAN θ
1)
State the two angles between 0° and 360° for each of these tangent values:
(a)
0.8
(c)
(b)
0.3
0.1
(d)
0.9
(f)
(e)
0.682
0.35
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TRIGONOMETRIC ANGLES
TASK 8 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ
1)
State the two angles between 0° and 360° for each of these values:
(a)
sine of 0.1
(c)
(b)
tangent of 0.5
cosine of 0.8
(d)
cosine of 0.6
(f)
(e)
sine of 0.9
tangent of 0.4
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TRIGONOMETRIC ANGLES
TASK 8 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ
2)
State the two angles between 0° and 360° for each of these values:
(a)
sine of 0.27
(c)
(b)
tangent of 0.12
cosine of 0.62
(d)
Cosine of 0.86
(f)
(e)
sine of 0.38
tangent of 0.75
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TASK 8 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ
3)
State the two angles between 0° and 360° for each of these values:
(a)
sine of 0.3
(c)
(b)
tangent of 0.8
cosine of 0.5
(d)
cosine of 0.6
(f)
(e)
sine of 0.4
tangent of 0.2
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TASK 8 (GRADE A*) – MIXTURE OF SIN θ, COS θ & TAN θ
4)
State the two angles between 0° and 360° for each of these values:
(a)
sine of 0.46
(c)
(b)
tangent of 0.69
cosine of 0.62
(d)
cosine of 0.24
(f)
(e)
sine of 0.84
tangent of 0.48
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TRIGONOMETRIC ANGLES
EXTENSION 2 (GRADE A*) – WITHOUT A CAST DIAGRAM
1)
State the two angles between 0° and 360° for each of these values:
(a)
sine of 0.5
(c)
(b)
tangent of 0.7
cosine of 0.2
(c)
cosine of 0.8
(e)
(d)
sine of 0.1
tangent of 0.5
(f)
tangent of 0.12
(h)
(g)
cosine of 0.91
sine of 0.83
(i)
sine of 0.47
(k)
(j)
sine of 0.72
tangent of 0.22
(l)
sine of 0.462
(n)
(m)
tangent of 0.836
cosine of 0.673
(o)
cosine of 0.6
(q)
(p)
sine of 0.8
tangent of 0.4
(r)
tangent of 0.3
(t)
(s)
sine of 0.5
cosine of 0.9
(u)
sine of 0.63
(w)
(v)
tangent of 0.94
cosine of 0.26
(x)
cosine of 0.13
(z)
(y)
sine of 0.71
tangent of 0.47