4 3 Trigonometry Extended The Circular Functions Free

4. 3 Trigonometry Extended: The Circular Functions Free Powerpoint Templates Page 1

Angle Standard Position • Positive angle (rotate counterclockwise) • Negative Angle (rotate clockwise) Free Powerpoint Templates Page 2

Coterminal Angles Coterminal angles are angles in standard position that have a common terminal side • To find a positive or negative coterminal angle add or subtract 360°. • If the angle is measured in radians, then add/subtract 2π Free Powerpoint Templates Page 3

Finding coterminal angles Find a positive and negative coterminal angle for the given angles: 1) 30 2) -150 3) 2π/3 Free Powerpoint Templates Page 4

Angles and (x, y) coordinates in the Cartesian Plane Free Powerpoint Templates Page 5

The point (3 , 4) is on the terminal side of angle θ. Evaluate the six trigonometric functions for θ. sin θ= csc θ= cos θ= sec θ= tan θ= cot θ= Free Powerpoint Templates Page 6

You Try! The point (5, -2) is on the terminal side of angle θ. Evaluate the six trigonometric functions for θ. sin θ= csc θ= cos θ= sec θ= tan θ= cot θ= Free Powerpoint Templates Page 7

Trig Functions of any Angle sin θ= csc θ= cos θ= sec θ= tan θ= cot θ= Free Powerpoint Templates Page 8

Find the six trig functions of 315° sin 315°= csc 315°= cos 315°= sec 315°= tan 315°= cot 315°= Free Powerpoint Templates Page 9

Find sin (-210°) without a calculator: You Try! Find cos (-210°) and cot (-210°) without a calculator: Free Powerpoint Templates Page 10

Find the value of tan 3π You Try! Find the value of sin 3π and cos 3π Free Powerpoint Templates Page 11

Using one trig ratio to find the others Ex) sin θ = 3/7 and tan θ < 0 Free Powerpoint Templates Page 12

Unit Circle A circle of radius 1 centered at the origin Free Powerpoint Templates Page 13

Trig Functions of Real Numbers sin t= csc t= cos t= sec t= tan t= cot t= Free Powerpoint Templates Page 14

Periodic Functions A function y =f(t) is periodic if there is a positive number c such that f (t + c) = f(t) for all values of t in the domain of f. The smallest such number c is called the period of the function. A periodic function repeats itself at regular intervals. Sine and Cosine functions have period 2 π and the tangent function has period π Find the value without a calculator of: Free Powerpoint Templates Page 15

Unit Circle Free Powerpoint Templates Page 16

Quiz Study Guide • Converting angles from DMS to decimal degrees( and decimal degrees to DMS) • Converting from radians to degrees (and degrees to radians) • Using the arc length formula • Finding an angle degree for a specific compass bearing • Angular and Linear Speed Problems (Unit Conversions) • Given the sin of an angle θ, find cosine of θ • Using reference triangles • Finding Positive and Negative coterminal Angles Free Powerpoint Templates Page 17