Concepts Examples 0 x y 5p 4 7p 4 3p 4 y = sec(x + )P 4 p 4 p 4 – –1 1 period: 2p phase shift: left p 4 unit domain: Ex x ≠p 4 + np, where n is any integerF range: 1-∞, -14 ´31, ∞2 Secant and Cosecant Functions Graph y = sec Ax + p 4 B over a one-period interval. A spring oscillates according to s1t2 = -5 cos 6t, where t is in seconds and s1t2 is in inches. Find the amplitude, period, and frequency. amplitude = -5 = 5 in. period = 2p 6 = p 3 sec frequency = 3 p oscillation per sec 6.6 Graphs of the Secant and Cosecant Functions x y 0 y = sec x 1 –1 –p 2 p –p p 2 Do main: Ex x ≠12n + 12 p 2 , where n is any integerF Range: 1-∞, -14 ´31, ∞2 Period: 2p x y 0 y = csc x 1 –1 –p 2 p p –p 2 Domain: 5x x ≠np, where n is any integer6 Range: 1-∞, -14 ´31, ∞2 Period: 2p 6.7 Harmonic Motion Simple Harmonic Motion The position of a point oscillating about an equilibrium position at time t is modeled by either s1t2 =a cos V t or s1t2 =a sin V t, where a and v are constants, with v70. The amplitude of the motion is a , the period is 2p v , and the frequency is v 2p oscillations per time unit. 671 CHAPTER 6 Review Exercises Concept Check Work each problem. 1. What is the meaning of “an angle with measure 2 radians”? 2. Consider each angle in standard position having the given radian measure. In what quadrant does the terminal side lie? (a) 3 (b) 4 (c) -2 (d) 7 3. Find three angles coterminal with an angle of 1 radian. 4. Give an expression that generates all angles coterminal with an angle of p 6 radian. Let n represent any integer. Chapter 6 Review Exercises
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