3.6 Functions of Special & Quadrantal Angles

The key DRAW THE ANGLE & TRIANGLE!!

Quadrantal angle = angle with terminal side on x- or y-axis

Ex 1) Find the exact values of the six trig functions.

01

sin 0

cos 1

tan 0

2

a) θ = 360° 10

11

10

csc undefined

sec 1

cot undefined

b)

10

sin 1

cos 0

tan undefined

11

10

01

csc 1

sec undefined

cot 0

Let’s fill out the rest on our chart!

The other special/ famous angles come from special right triangles

45°

45°

legs are the samePythag sayshypotenuse is 2

1

1

2

want hyp = 1so divideeverything by 2

22

2

2

2

2

2

45°

45°

Now

1

60°

30°

start w/ short leghyp = 2long leg = 3

12

3

want hyp = 1so divideeverything by 2

2

2

2

1

2

3

2

60°

30°

Now: 1

60°

30°

1

2

3

21

OR:

We make these triangles wherever we need to!

Reference Angle: the acute angle formed by terminal side of θ and the x-axisYou could memorize the rules

Ex 2) Find the reference anglea) –390º

4

3

3

Or just draw a picture!

b)

30°

Use the reference angle to make your triangle!

Ex 3) Use reference angle & find sinθ, cosθ, & tanθa) 150º

1sin

2

3cos

2

1

2

b)

150°

30°3

2

112

32

1 3 3tan

33 3

5

4

2

2

45°

2

2

1

2sin

2

2cos

2

22

22

tan 1

Ex 3) Use reference angle & find sinθ, cosθ, & tanθ

c)

3sin

21

cos2

1

2

Ex 4) If 0 ≤ θ ≤ 2π, determine the values of θ for which

60°3

2

1

32

12

tan 3

3

30°

1sin

2

3065

1506

y = sinθ is (+) in I & IIdraw some short △s

30°

150°

Let’s tackle the rest of our unit circle & chart!

Homework#306 Pg 157 #1–49 odd