Chapter Test For 12e Swokowski/Cole-Agebra and Trigonometry with Analytic e and
ID: 3121920 • Letter: C
Question
Chapter Test For 12e Swokowski/Cole-Agebra and Trigonometry with Analytic e and coe P for a second quadrant angle a and a third quadrant angle tan If cos (a cosa cost sino ginb 8. Use an addition or subtraction formula to find the solutions of the equation that are in the interval t sin 5t cos 2t sin 2t cos 5t Sin toos, 2t sin (Et-2t) o 9. Use an addition or subtracton formula to find the solutions of the equation that are in the interval t tan 6 tan 3t 10. Use the formula acos Be bsin Be Acos Be where A b and tan c e with C to determine the period off(). 11. Find the exact values of sin 28, cos 25, and tan 29 for the given values of e cos e 17 90 24O 20a 384Explanation / Answer
(The policy in Chegg allows to answer only four questions. Please post a new question for remaining answers)
7. tan = -7/24 cot = 3/4
sin = 7/(242+72) = 7/25 (Given is in second quadrant)
cos = -24/25
sin = -4/(32+42) = -4/5 (Given is in third quadrant)
cos = -3/5
cos ( + ) = cos cos - sin sin
= (-24/25 * -3/5) - (7/25 * -4/5)
= 100/125 = 4/5.
8. sin5t cos2t = sin2t cos5t
=> sin5t cost2t - sin2t cos5t = 0
=> sin(5t-2t) = 0
=> sin 3t = 0
=> 3t = 0, 3t = and 3t = 2
=> t = 0, /3 and 2/3.
9. tan 3t - tan 6t = 1+ tan 6t tan 3t
=> (1+ tan 6t tan 3t) / (tan 3t - tan 6t) = 1
=> tan(3t-6t) =1
=> tan -3t =1
=> -3t = /4 or 5/4
=> t = -/12 and t = -5/12
=> t = 11/12 and t = 7/12
(Note t = /4 => tan 6t = tan 3/2 = )
10. Applying the formula
f(x) = 2 cos 4x - 2 sin 4x
= (22+22) cos(4x - C) (tan C = 2/-2 = -1)
Since tan C = -1 and -/2 < C < /2, C = -/4
f(x) = 22 cos(4x- (-/4))
= 22 cos(4x + /4))
Period of cos x is 2. So period of cos 4x is /2. The period of cos 4x+/4 is also /2 since /4 is a constant.