SOLUTION: solve each of the following cos theta=-3sin theta 3cos^2theta=5-7sin theta

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Question 261882: solve each of the following
cos theta=-3sin theta
3cos^2theta=5-7sin theta
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
cos_theta=-3sin_theta
step 1 - divide by cos theta to get
1+=+-3tan_theta
step 2 - divde by -3 to get
%28-1%2F3%29+=+tan_theta
step 3- take arctan to get
theta+=+arctan%28-1%2F3%29
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3cos%5E2+%28theta%29=5-7sin_%28theta%29
step 1 - use the identity sin^2(theta) + cos^2(theta) = 1 to get
3%281+-+cos%5E2+%28theta%29%29+=+5+-+7+sin_%28theta%29
step 2 - distribute the 3 to get
3+-+3+sin%5E2+%28theta%29+=+5+-+7+sin_%28theta%29
step 3 - set = 0 to get

step 5 - set = 0 and solve for theta to get
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%283sin_%28theta%29+-1%29+=+0
sin_%28theta%29+=+1%2F3
theta+=+arcsin%281%2F3%29
---
sin_%28theta%29+-2+=+0
sin_%28theta%29+=+2
but this is not possible, so our answer is:
theta+=+arcsin+%281%2F3%29