SOLUTION: Solve 3 sin θ = 4 cos θ for all nonnegative values of θ less than 360°. Give answers in increasing order. All values should be in degrees. Round to one decimal pl

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Question 1068406: Solve 3 sin θ = 4 cos θ for all nonnegative values of θ less than 360°.
Give answers in increasing order. All values should be in degrees. Round to one decimal place.
Found 2 solutions by Fombitz, ikleyn:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
3sin%28theta%29=4cos%28theta%29
9sin%5E2%28theta%29=16cos%5E2%28theta%29
9sin%5E2%28theta%29=16%281-sin%5E2%28theta%29%29
9sin%5E2%28theta%29=16-16sin%5E2%28theta%29
25sin%5E2%28theta%29=16
sin%5E2%28theta%29=16%2F25
sin%28theta%29=0+%2B-+4%2F5
theta=53.3 and theta=126.7
and
theta=233.1 and theta=306.9
Verify these solutions and you'll see that there are really only 2 solutions not 4.

Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
.
Solve 3 sin θ = 4 cos θ for all nonnegative values of θ less than 360°.
Give answers in increasing order. All values should be in degrees. Round to one decimal place.
~~~~~~~~~~~~~~~~~~~ 

3sin%28theta%29 = 4cos%28theta%29  --->  tan%28theta%29 = 4%2F3.


theta = arctan%284%2F3%29   and  theta = arctan%284%2F3%29 + 180 degs.


Use your calculator to find arctan%284%2F3%29.


That's all.

For your info: this all is about the angle of a right angled triangle 3-4-5.