5.2 Trigonometric Functions

Sine, Cosine, Tangent, Cosecant, Secant, Cotangent

ry

x

siny

r

Sine

ry

x

cosx

r

Cosine

ry

x

tany

x

Tangent

sintan

cos

ry

x

cscr

y

Cosecant

1csc

sin

ry

x

secr

x

Secant

1sec

cos

ry

x

cotx

y

Cotangent

coscot

sin

Review - Special Right Triangles

21

1

45 30

3

2 1

60

32

1

454

603

306

You MUST know these!

Find the exact value of the trig functions for the given angle

315 Quadrant IV

Find the exact value of the trig functions for the given angle

315

Reference Angle 45⁰

Find the exact value of the trig functions for the given angle

315

45

Find the exact value of the trig functions for the given angle

315

45

Find the exact value of the trig functions for the given angle

315

45

2-1

1

1sin 315

2

1 2sin 315

2 2

2sin315

2

Find the exact value of the trig functions for the given angle

315

45

2-1

1

1cos315

2

1 2cos315

2 2

2cos315

2

Find the exact value of the trig functions for the given angle

315

45

2-1

1

1tan315

1

tan315 1

Find the exact value of the trig functions for the given angle

315

45

2-1

12

csc3151

csc315 2

Find the exact value of the trig functions for the given angle

315

45

2-1

12

sec3151

sec315 2

Find the exact value of the trig functions for the given angle

315

45

2-1

1

1cot 315

1

cot 315 1

Find the exact value of the trig functions for the given angle

5

6

Quadrant II

306

3

12

5sin

6

5cos

6

5tan

6

5csc

6

5sec

6

5cot

6

Find the exact value of the trig functions for the given angle

5

6

306

3

12

5 1sin

6 2

5 3cos

6 2

5 3tan

6 3

5csc 2

6

5 2 3sec

6 3

5cot 3

6

The angle measures that place the terminal ray on one of the axes.

Degrees - 0⁰, 90⁰, 180⁰, 270⁰, 360⁰, …

Radians – 0, π/2, π, 3π/2, 2π, …

For these, draw and label a point 1 unit from the origin to find the values of the trigonometric functions.

Quadrantal Angles

(-1,0)

r=1

sin

cos

tan

csc

sec

cot

01

11

01

0

1

0

10

11

10

1

Assignmentp. 384 # 51 - 66 multiples of 3

Using your Calculator… Set MODE according to how the angle is

measured (“degrees” or “radians”)

Use the SIN, COS, or TAN keys

Close parentheses after the angle measure

cos14

cos14 0.97

10sin

10sin 0.31

csc37

csc37 1.66

csc37

csc37 1.66

Alternative

If (-5,12) is on the terminal side, find the exact value of the six trig functionsQuadrant II

(-5,12)

-5

12 13

sin

cos

tan

csc

sec

cot

1213

513

12 125 5

1312

13 135 5

512

If (2,-1) is on the terminal side, find the exact value of the six trig functionsQuadrant IV

(2,-1)

-1

2

sin

cos

tan

csc

sec

cot

55

2 55

12

52

5

2

5

Assignmentp. 384 # 69 - 81 multiples of 3, 83 - 92