Trigonometry Overview, calculus homework help

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Consider the right triangle ABC given below: (a) Find the length of side b to two decimal places. (b) Find the length of side a to two decimal places in three different ways. Answer: If the arc length shown is 15 feet, find  to the nearest hundredth of a degree. Answer: For the functions below, state the amplitude, period, phase shift, and vertical translation of the graph for the sinusoid.   (c) y   sin  x    2 4  (d) y  2cos  2x  Answer: (e) Amplitude: Period: Phase Shift: Vertical Translation: (f) Amplitude: Period: Phase Shift: Vertical Translation: An object's motion is described by the equation d  4sin  t  . The displacement, d, is measured in meters. The time, t, is measured in seconds. Answer the following questions: (g) What is the object's position at t = 0? (h) What is the object's maximum displacement from its resting position? (i) How much time is required for one oscillation? (j) What is the frequency? Answer: Solve each equation on the interval 0,2 Answer: (k) 4sin2 x  3  0 (l) cos  3x   1  17  Use the half-angle formula to evaluate: tan    12  Answer: Prove the identity: sin  2 x  sin x  cos  2 x  cos x  sec x Answer: Calculation Reason Solve the triangles below. a.) b.) Answer: Consider the vector v   5, 8 . a.) What is the angle between v   5, 8 and the positive x-axis? b.) Write v in the form  v cos , v sin  . Answer: Use De Moivre’s Theorem to compute the following:     i sin 27  a.) 3 cos 27  b.) 3 5   4   4   8  cos    i sin  5   5      Answer: Use w and z to solve. 5 3 5  i 2 2 . w  1  3i z a.) Convert z and w to polar form. b.) Calculate zw. c.) Calculate Answer: z . w
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Consider the right triangle ABC given below:

(a) Find the length of side b to two decimal places.
(b) Find the length of side a to two decimal places in three different ways.
Answer:

If the arc length shown is 15 feet, find θ to the nearest hundredth of a degree.

Answer:

For the functions below, state the amplitude, period, ph...


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