More Trig – Angles of RotationLearning Objective: To find coterminal and reference angles and the trig

function values of angles in standard position

Warm-up (IN)

Notes

Learning Objective: To find coterminal and reference angles and the trig function values of angles in standard position

Initial side - the first side of an angle, usually on the x-axis

Terminal side - the other side - in the counter-clockwise direction of the initial side.

Vertex - the point where the rays intersect and if it lies on the origin, the angle is in standard position.

**Negative angles go from initial to terminal in a clockwise direction

Learning Objective: To find coterminal and reference angles and the trig function values of angles in standard position

Ex 1 - Draw each Angle

a) 45º b) -90º c) 225º

d) 405º e) -150º

Learning Objective: To find coterminal and reference angles and the trig function values of angles in standard position

Coterminal angles -Angles in standard position that have the same terminal side

135°

-225°

495°

Ex 2 - Find the coterminal angle, , for each angle such that

a) 90º b) -210º

360 360

Add and subtract 360° from each angle

90°+360°=

450°

90°-360°=

-270°

-210°+360°=

150°

-210°-360°=

-570°

The acute angle that is formed by the terminal side of Θ and either the positive or negative x-axis

Learning Objective: To find coterminal and reference angles and the trig function values of angles in standard position

Reference angle -

ref

In quadrants I and IV, use positive x-axis

In quadrants II and III, use negative x-axis

Ex 3 – Find the reference angle, , for each:

a. 212

32

Learning Objective: To find coterminal and reference angles and the trig function values of angles in standard position

ref

180 212b. 340

20

Use the coterminal angle when negative

c. 40

40

d. 124

56

180 124e. 110

70

180 250Coterminal is 250

f. 290

360 290

70

HW –

Out – How many angles in standard position between 0° and 360° have the same reference angle? Explain.

Summary – I think…