8.4 Trigonometric Ratios- Sine and Cosine

[Pages:22]8.4 Trigonometric

Ratios- Sine and

Cosine

Geometry Mr. Peebles Spring 2013

Daily Learning Target (DLT)

Wednesday April 17, 2013

? "I can apply my knowledge of right triangles to find the sine and cosine of an acute angle."

Trigonometric Ratios

? Let ABC be a right

triangle. The since,

the cosine, and the hypotenusec tangent of the

acute angle A are

defined as follows. A

b side adjacent to angle A

B

Side a opposite

angle A

C

sin A = Side opposite A hypotenuse

cos A = Side adjacent to A= b

= a

hypotenuse

c

c tan A = Side opposite A = a

Side adjacent to A b

Trigonometric Ratios

? TOA ? CAH ? SOH

Tangent = Opposite/Adjacent Cosine = Adjacent/Hypotenuse Sine= Opposite/Hypotenuse

Trigonometric Ratios

? TOA ? SOH ? CAH

"Together Only Actors Sing On Holidays Cheering All Happily."

Ex. 1: Finding Trig Ratios

Large

Small

opposite sin A =

hypotenuse

adjacent cosA =

hypotenuse

17

A

15

B

B

8.5

8

4

A

7.5

C

C Trig ratios are often

expressed as decimal approximations.

Ex. 1: Finding Trig Ratios

Large

Small

opposite sin A =

hypotenuse

adjacent cosA =

hypotenuse

8 0.4706 17

15 0.8824 17

4 0.4706 8.5

7.5 0.8824 8.5

17

A

15

B

B

8.5

8

4

A

7.5

C

C Trig ratios are often

expressed as decimal approximations.

Ex. 2: Finding Trig Ratios

opposite sin S =

hypotenuse

adjacent cosS =

hypotenuse

S

R

opposite 5

13 hypotenuse

T

12

S

adjacent

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