Find all 6 trig ratios from the given information.1.

2. sinθ = 8/13 3. cotθ = 5

Warm Up May 5th

9

15

Trig on a Coordinate Plane & Angles

An angle is formed by the rotation of a ray about its endpoint.

The starting position is the initial side and the position after rotation is the terminal side.

A reference angle is the acute angle formed by the terminal side of an angle in standard position (when it’s vertex is at the origin) and the x-axis.

Trig on a Coordinate Plane

Let (6, 8) be a point on the terminal side of . Find all six trig ratios.

Examples

Let (-5, -12) be a point on the terminal side of . Find all six trig ratios.

Examples (cont.)

Find the values of the 6 trig functions of . Examples (cont.)

IVquadrant in lies and 5

2tan

Degrees are based on fractional parts of a circular revolution.

Degrees

Radian measure compares the length of an arc that a central angle cuts off to the radius of the circle.

Radians

To convert degrees to radians:60° -120°

To convert radians to degrees:(7/12)π

Degree & Radian Conversions

Convert degrees to radians and radians to degrees.

-45º 210º 684º

Conversion Practice

AnglesPositive Negative Wrapping

Determine the quadrant in which the angle lies and sketch the angle in standard position. Then state the reference angle.

1) 100°

2) -290°

3) 520°

4) 9π/55) -3π/76) 10π/37) -2

Angles in standard position whose terminal sides coincide are called coterminal angles.

Determine two coterminal angles (one negative and one positive) for each given angle.1) 140○

2) 3π/7

Warm Up May 6th Write down the first 10 multiples of the following:1. 30:2. 45:3. 1/6:4. 1/4:5. With a hypotenuse of 1, find the legs.

30○

60○

45○

45○

Homework Questions?

The Unit Circle:

a circle with radius 1 and center at the

origin

30 Degree Reference Angle

60 Degree Reference Angle

45 Degree Reference Angle

Don’t Forget the Radians!

Using The Unit CircleFind the point on the unit circle that corresponds to the angle.1) 120○ 2) 225○ 3) 330 ○

4) 5) 6) 6

53

2

3

Using The Unit Circle – tougher Find the point on the unit circle that corresponds to the angle.1) -210○ 2) 675○ 3) -540 ○

4) 5) 6) 3

5

6

232

11

What does this have to do with Trig?

1. Sin30

2. Cos90

3. Sin135

4. Cos120

5. Sin 180

6. Cos225

7. Sin240

8. Cos270

9. Sin315

10. Cos330

Unit Circle Practice

1. Sin30

2. Cos90

3. Sin135

4. Cos120

5. Sin 180

6. Cos225

7. Sin240

8. Cos270

9. Sin315

10. Cos330

Unit Circle Practice - tougher

Other Trig Functions and their relationship to sine/cosine

sincsc

cossec

tansin

coscot

cos

sintan

1

1

1or

More Unit Circle PracticeEvaluate each of the following.1. tan(240○) 2. csc(225○)

3) cot(2π/3) 4) sec(π/4)

A ton of practice…