Warm up

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# Warm up - PowerPoint PPT Presentation

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
• State the domain for:
• If f(x) = x3 – 2x +5 find f(-2)

### Right Triangle Trigonometry

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

SINE

Prounounced “sign”

COSINE

Prounounced “co-sign”

TANGENT

Prounounced “tan-gent”

Greek Letter q

Prounounced “theta”

Represents an unknown angle

hypotenuse

hypotenuse

opposite

opposite

Some

Old

Hippie

Came

A

Hoppin’

Through

Our

Old Hippie

Apartment

Sin

SOHCAHTOA

Opp

Hyp

Cos

Hyp

Tan

Opp

Old Hippie

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

Find the values of the three trigonometric functions of .

?

Pythagorean Theorem:

5

4

(3)² + (4)² = c²

5 = c

3

Sine
• Find the sin of α

β

8

α

A

10

C

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
• Find the cosine and tan of α

β

6

5

α

A

√11

C

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

β

5

3

α

A

4

C

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 Cosine
• (adj)2+ (opp)2= 1
• (hyp)2 (hyp)2
• (sin (x))2 + (cos (x))2 = 1
• sin2(x) + cos2(x) = 1