Find the general solution to the following equations. Give your answers as the s

Question

Find the general solution to the following equations. Give your answers as the smallest number greater than zero plus a multiple of a (do not approximate). Enter the smaller number first and the larger number second. If the answer can be expressed using only one answer box, enter DNE in the empty answer boxes and choose the smallest correct number for the first box. (a) sin(2x) = ? x = X = Submit Answer Tries 0/99 (b) sin(4x) = -1 X = X = Submit Answer Tries 0/99 (c) cot(x) = v3 X = CITS ET x = Submit Answer Tries 0/99 (d) sec(3x) = 2 x = x = Submit Answer Tries 0/99 (e) sin(x) = -V x= x= Submit Answer Tries 0/99

Explanation / Answer

A) sin(2x)=1/2

2x=?/6

x=?/12

so the general solution is x=?/12+k?

k? because of the period of sin(2x)=?

B)sin4x=-1

4x=3?/2

x=3?/8

so the general solution is x=3?/8+k?/2

k?/2 because of the period of sin(4x)=?/2

C)cot(1/2)x=?3

(1/2)x=?/6

x=?/3

so the general solution is x=?/3+2k?

2k? because of the period of cot(1/2x)=2?

D)sec(3x)=2

3x=?/3

x=?/9

so the general solution is x=?/9+2k?/3

2k?/3 because of the period of sec(3x)=2?/3

E)sin(1/3x)=-?3/2

x/3=4?/3

x=4?

so the general solution is x=4?+6k?

6k? because of the period of sin((1/3)x)=6?

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