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Warm up. State the domain for : If f(x) = x 3 – 2x +5 find f(-2). Right Triangle Trigonometry. Objective To learn the trigonometric functions and how they apply to a right triangle. The Trigonometric Functions we will be looking at. SINE. COSINE. TANGENT. The Trigonometric Functions.

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Presentation Transcript
warm up
Warm up
  • State the domain for:
  • If f(x) = x3 – 2x +5 find f(-2)
right triangle trigonometry

Right Triangle Trigonometry

Objective To learn the trigonometric functions and how they apply to a right triangle.

slide5

SINE

Prounounced “sign”

slide6

COSINE

Prounounced “co-sign”

slide7

TANGENT

Prounounced “tan-gent”

slide8

Greek Letter q

Prounounced “theta”

Represents an unknown angle

slide9

hypotenuse

hypotenuse

opposite

opposite

adjacent

adjacent

slide11

Some

Old

Hippie

Came

A

Hoppin’

Through

Our

Old Hippie

Apartment

slide12

Sin

SOHCAHTOA

Opp

Hyp

Cos

Adj

Hyp

Tan

Opp

Adj

Old Hippie

slide15

Find the sine, the cosine, and the tangent of angle A.

Give a fraction and decimal answer (round to 4 places).

10.8

9

A

6

slide16

Find the values of the three trigonometric functions of .

?

Pythagorean Theorem:

5

4

(3)² + (4)² = c²

5 = c

3

slide17
Sine
  • Find the sin of α

β

8

α

A

10

C

slide18

Find the sine, the cosine, and the tangent of angle A

Give a fraction and decimal answer (round to 4 decimal places).

B

24.5

8.2

A

23.1

cosine
Cosine
  • Find the cosine and tan of α

β

6

5

α

A

√11

C

relationship between sine and cosine
Relationship between Sine and Cosine
  • Sin (α) = cos ( )

β

5

3

α

A

4

C

relationship between sine and cosine1
Relationship between Sine and Cosine
  • Look at the Pythagorean Theorem
  • (adj)2 + (opp)2 = (hyp)2
  • Divide each side by (hyp)2
  • (adj)2+ (opp)2= (hyp)2
  • (hyp)2 (hyp)2 (hyp)2
relationship between sine and cosine2
Relationship between Sine and Cosine
  • (adj)2+ (opp)2= 1
  • (hyp)2 (hyp)2
  • (sin (x))2 + (cos (x))2 = 1
  • sin2(x) + cos2(x) = 1