644 CHAPTER 6 The Circular Functions and Their Graphs 1. Convert 225° to radians. 2. Convert - 7p 6 to degrees. A central angle of a circle with radius 300 in. intercepts an arc of 450 in. (These measures are accurate to the nearest inch.) Find each measure. 3. the radian measure of the angle 4. the area of the sector Find each exact circular function value. 5. cos 7p 4 6. sin a- 5p 6 b 7. tan 3p 8. Find the exact value of s in the interval C p 2 , pD if sin s = 23 2 . 9. Give the amplitude, period, vertical translation, and phase shift of the function y = 3 - 4 sin A2x + p 2 B . Graph each function over a two-period interval. Give the period and amplitude. 10. y = -4 sin x 11. y = - 1 2 cos 2x 12. y = -2 cos ax + p 4b 13. y = 2 + sin12x - p2 Connecting Graphs with Equations Each function graphed is of the form y = a cos bx or y = a sin bx, where b 70. Determine an equation of the graph. 14. x y –2 0 2 2p p 15. x y –1 0 1 p p 2 Chapter 6 Quiz (Sections 6.1– 6.4) 6.5 Graphs of the Tangent and Cotangent Functions ■ Graph of theTangent Function ■ Graph of the Cotangent Function ■ Techniques for Graphing ■ Connecting Graphs with Equations Graph of the Tangent Function Consider the table of selected points accompanying the graph of the tangent function in Figure 41 on the next page. These points include special values between - p 2 and p 2 . The tangent function is undefined for odd multiples of p 2 and, thus, has vertical asymptotes for such values. A vertical asymptote is a vertical line that the graph approaches but does not intersect. As the x-values get closer and closer to the line, the function values increase or decrease without bound. Furthermore, because tan1-x2 = -tan x, Odd function the graph of the tangent function is symmetric with respect to the origin.
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