Geometry Honors Name________________________________ 9.9 Notes Seitz Bugajsky

GOAL:

To be able to evaluate and use trigonometric functions to find side lengths and angle measures.

Part I: Definitions

Opposite side: Adjacent side: Hypotenuse:

New Vocab: sine of x cosine of x tangent of x

Written as:

sinx

cos x

tanx

O A OH H A

OH AH OAS C TS C T

pposite

ypotenuse

O

Hine S In this case:

sin A

djacent

ypotenuse

A

Hosine C In this case:

cos A

pposite

djacent

O

Aangent T In this case:

tan A

**HUGE HINTS:

The word opposite means “across from” and adjacent means “next to” You will never find the trig function of a right angle, only the acute angles.

Remember that " "x is the degree measure of an acute .

Example 1: Find sin , cos , tan , sin , cos and tan .P P P Q Q Q

sin ______P cos _______P tan ______P

sin ______Q cos _______Q tan ______Q

Trigonometric ratio:

The ratio of the of a ______________________.

B

P 5

13

Q

R

A

4

3

C

C

A

B

Example 2: Find sin , cos , tan , sin , cos and tan .P P P Q Q Q

sin 60 ______ cos60 _______ tan 60 ______

sin30 ______ cos30 _______ tan30 ______

Example 3: If 7

cos24

Q , find tanV Example 4: Find sin Q

Part II Solving Trig Equations Most importantly, we use these trigonometric ratios to SOLVE for other parts on triangles.

SCENARIO 1: Finding a side and x is in the numerator of the ratio.

x

sin347

SCENARIO 2: Finding a side and x is in the denominator of the ratio.

6

tan71x

EX #1: Find x. Round to the nearest tenth. EX #2: Find x. Round to the nearest

tenth.

EX #3: Find y. Round to the nearest tenth. EX #4: Find y. Round to the nearest

tenth.

10

32º

x

Y 12

6 71º

x

y

31º

76 y

40º

28

60

P

Q

R

Q

T

10

10