SOLUTION: 12) for x E[0,2pi), solve sin x = cos x a) pi/2 , 3pi/2 b) pi/4 , 5pi/4 c) pi/4 , 3pi/4 d) 3pi/4 , 7pi/4 e) None of these

Algebra ->  Trigonometry-basics -> SOLUTION: 12) for x E[0,2pi), solve sin x = cos x a) pi/2 , 3pi/2 b) pi/4 , 5pi/4 c) pi/4 , 3pi/4 d) 3pi/4 , 7pi/4 e) None of these       Log On


   

Question 122526: 12) for x E[0,2pi), solve sin x = cos x

a) pi/2 , 3pi/2
b) pi/4 , 5pi/4
c) pi/4 , 3pi/4
d) 3pi/4 , 7pi/4
e) None of these

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 12

sin%28x%29=cos%28x%29 Start with the given equation


sin%28x%29%2Fcos%28x%29=1 Divide both sides by cos%28x%29


tan%28x%29=1 Rewrite the left side using the identity tan%28x%29=sin%28x%29%2Fcos%28x%29



x=arctan%281%29 Take the arctangent of both sides to isolate x


x=pi%2F4 or x=5pi%2F4 Take the arctangent of 1 to get pi%2F4 or 5pi%2F4



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Answer:

So the solutions are

x=pi%2F4 or x=5pi%2F4

which means that the answer is B)