Try this... 1. Locate the vertical asymptotes and sketch the graph of y = 2 sec x. 2. Locate the vertical asymptotes and sketch the graph of y = 3 tan.

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Presentation transcript:

Try this Locate the vertical asymptotes and sketch the graph of y = 2 sec x. 2. Locate the vertical asymptotes and sketch the graph of y = 3 tan 2x.

Inverse Trig Functions Mastery Objectives Evaluate and graph inverse trigonometric functions. Find compositions of trigonometric functions.

Vocabulary arcsine function arccosine function arctangent function

Arcsine, sin -1 a

Find the exact value of, if it exists.

Answer:

Find the exact value of, if it exists.

Answer: CHECK If arcsin then sin

Find the exact value of sin –1 (–2π), if it exists. Answer:does not exist

Find the exact value of sin –1 0. A.0 B. C. D. π

Arccosine, cos -1 a

Find the exact value of cos –1 1, if it exists. Find a point on the unit circle on the interval [0, π] with an x-coordinate of 1. When t = 0, cos t = 1. Therefore, cos –1 1 = 0.

Answer: 0 Check If cos –1 1 = 0, then cos 0 = 1.

Find the exact value of, if it exists.

CHECK If arcos Answer:

Find the exact value of cos –1 (–2), if it exists. Answer: does not exist

Find the exact value of cos –1 (–1). A. B. C. π D.

Warm Up...

Arctangent, tan -1 a

Find the exact value of, if it exists.

Answer: Check If, then tan

Find the exact value of arctan 1, if it exists.

Answer: Check If arctan 1 =, then tan = 1.

Find the exact value of arctan. A. B. C. D.

Inverse Trig Functions

Domains of Trig Functions

Find the exact value of, if it exists. Therefore, The inverse property applies because lies on the interval [–1, 1]. Answer:

Find the exact value of, if it exists. Notice that does not lie on the interval [0, π ]. However, is coterminal with or which is on the interval [0, π ].

Therefore,. Answer:

Answer: does not exist Find the exact value of, if it exists. Because tan x is not defined when x =, arctan does not exist.

Find the exact value of arcsin A. B. C. D.

Find the exact value of Because the cosine function is positive in Quadrants I and IV, and the domain of the inverse cosine function is restricted to Quadrants I and II, u must lie in Quadrant I. To simplify the expression, let u = cos –1 so cos u =.

Using the Pythagorean Theorem, you can find that the length of the side opposite  is 3. Now, solve for sin u. opp = 3 and hyp = 5 Sine function So, Answer:

Find the exact value of A. B. C. D.

Write cot (arccos x) as an algebraic expression of x that does not involve trigonometric functions. Let u = arcos x, so cos u = x. Because the domain of the inverse cosine function is restricted to Quadrants I and II, u must lie in Quadrant I or II. The solution is similar for each quadrant, so we will solve for Quadrant I.

Answer:

Write cos(arctan x) as an algebraic expression of x that does not involve trigonometric functions. A. B. C. D.

Homework