<p>4.7 inverse Trigonometry Function Sine Function interval </p><p>1. the function is increasing. </p><p>2. </p><p>3. passes the Horizontal Line Test on the restricted domain has a unique inverse called the inverse sine function.</p><p>It is denoted by or x p p p p 0 p p p p - - - - 2 3 4 6 6 4 3 2 Y=sinx x Y=arcsinx Or sin-1 x Tangent Function interval </p><p>1. the function y= tan x is increasing. </p><p>2. -� < tan x</p><p>3. y= tan x passes the Horizontal Line Test</p><p> on the restricted domain y= tan x has a unique inverse called the inverse sine function.</p><p>It is denoted by y= arctan x or y=tan-1 x x p p p p 0 p p p p - - - - 2 3 4 6 6 4 3 2 Y=tanx x Y=arctanx Or tan-1 x</p><p>Cosine Function The cosine function is decreasing on the interval interval </p><p>1. the function y= cos x is decreasing. </p><p>2. -1＃ cosx 1</p><p>3. y= cos x passes the Horizontal Line Test</p><p> on the restricted domain has a unique inverse called the inverse cosine function.</p><p>It is denoted by y= arccos x or y=cos-1 x x 0 p p p p 2p 3p 5p p 6 4 3 2 3 4 6 Y=cosx x Y=arccosx Or cos-1 x Cotangent Function interval </p><p>1. the function y= cot x is decreasing. </p><p>2. -� < cot x</p><p>3. y= cos x passes the Horizontal Line Test on the restricted domain has a unique inverse called the inverse cosine function.</p><p>It is denoted by y= arccot x or y=cot-1 x x 0 p p p p 2p 3p 5p p 6 4 3 2 3 4 6 Y=cotx x Y=arccotx Or cot-1 x</p><p>Example 1 If possible, find the exact value. </p><p> c. </p><p> d. </p><p> e. </p><p> f. </p><p> g. </p><p> h. </p><p> i. </p><p>Example 2</p><p>Sketch a graph of y=arccotx Example 3 Use a calculator to approximate the value (if possible). a. b. c. </p><p>Properties If and then and </p><p>If and then and </p><p>If x is a real number and then and </p><p>Keep in mind that these inverse properties do not apply for arbitrary values of x and y. For instance,</p><p>In other words, the property is not valid for values of y outside the interval </p><p>EXAMPLE 4 Using Inverse Properties If possible, find the exact value. </p><p>=</p><p> d. </p><p> e. </p><p> f. </p><p>EXAMPLE 5 Find the exact value of </p><p>(a) and (b) </p><p>EXAMPLE 6 Write each of the following as an algebraic expression in x. a. </p><p> b. </p><p> c.</p><p>Summary: </p>