Bell Work

• Find all coterminal angles with 125°

• Find a positive and a negative coterminal angle with 315°.

• Give the reference angle for 212°.

5.2 Trigonometric Ratios in Right Triangles

Find the missing measures

X X 2.1

13 10.3

8

What is a ratio?

B

3 4

The ratio of side AB to side BC can be written as 3 to 4, 3:4, or ¾. (We will use the fraction form)

A C5

A comparison of two numbers

Trigonometric ratios

Sine (sin)

Cosine (cos)

Tangent (tan)

Cosecant (csc)

Secant (sec)

Cotangent (cot)

Trigonometric Ratios

B Sin C = Opposite

Hypotenuse

Cos C = Adjacent

Hypotenuse

Tan C = Opposite

Adjacent

AC

Find the values of the sine, cosine, and tangent for < B.

A

33

18

C B

Sin B = opposite =

hypotenuse

Cos B = Adjacent =

hypotenuse

Tan B = Opposite =

Adjacent

3√85

611

√85 11

6√85 85

Find the values of sine, cosine, and tangent for < A

B

15 8

A C

sin A =

Cos A =

tan A =

17

817

15 17

8 15

Reciprocal Trig Ratios

• What is a reciprocal?

• What is the reciprocal of ⅓?

• What is the reciprocal of ⅔?

• What is the reciprocal of ⅘?

Reciprocal Trig Ratios

• csc α = 1

sin α

• sec α = 1

cos α

• cot α = 1

tan α

NOTE: α represents an unknown angle measure

Reciprocal Trig Ratios

• If cos α = ½, then sec α = ____

• If sin α = ¾, then csc α = _______.

• If cot α = 2, then tan α= _______

2

4/3

½

Radical Review

√8

√588

7

√3

25

√15

Find the six trigonometric ratios for <P.

sin P = csc P =

cos P = sec P =

tan P = cot P =

P

M N

10

7

7√149 149

√149 7

10√149 149

√149 10

710

10 7

Find the six trigonometric ratios for <E.

sin E = csc E =

cos E = sec E =

tan E = cot E =

DE

F

7 3

3√58 58

7√58 58

37

73

√58 3

√58 7

Angle of Elevation

Special Right Triangles 30-60-90

5

5√3

Special Right Triangles 45-45-90

6

6

DEC 2007 ACT

F

EXIT PASS

Find the EXACT value.

1. cos A

2. tan B

3. csc A