Trigonometric Functions Section 1.6

Radian Measure The radian measure of the angle ACB at the center of the unit circle equals the length of the arc that ACB cuts from the unit circle.

Radian Measure An angle of measure θ is placed in standard position at the center of circle of radius r, In this course, you will see that so much of calculus only works when measuring angles in radians!!!

Trigonometric Functions of Theta

(1,0)(–1,0) (0,–1) (0,1)

Other Assortments… The graphs of cos x and sec x are even functions because their graphs are symmetric about the y-axis. The graphs of sin x, csc x, tan x and cot x are odd functions.

Inverse Trigonometric Functions None of the six basic trigonometric functions graphed in Figure 1.42 is one-to-one. These functions do not have inverses. However, in each case, the domain can be restricted to produce a new function that does have an inverse. The domains and ranges of the inverse trigonometric functions become part of their definitions.

Inverse Trigonometric Functions

A key to remember: Inverse trig functions ARE angles!!! “The sine (or other trig function) of what angle is x?” How to “read” inverse trig expressions… Also remember: Inverse sine and inverse tangent are always on the right half of the unit circle, and inverse cosine is always on the top half of the unit circle…

Guided Practice Evaluate each of the following:

Guided Practice Determine (a) the period, (b) the domain, and (c) the range, and (d) draw the graph of the function. Horizontal shift (phase shift) left, horizontal shrink by 1/4, vertical stretch by 2, vertical shift up 3 (a) Period: (b) Domain: (c) Range:(d) How does the graph look?

Guided Practice Solve the equation in the specific interval. n is any integer

Guided Practice Evaluate each of the following: Let’s complete this last one with an analytic graph…