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What is the value of x if pi le x le (3p...

What is the value of x if `pi le x le (3pi)/(2)` and `sinx=5cosx`?

A

3.399

B

6.625

C

4.515

D

4.623

Text Solution

Verified by Experts

The correct Answer is:
C
With your calculator in radian mode, plot of graphs of `Y_(1)=sinx and Y_(2)=5cosx` in a `[pi,(3pi)/(2)]` by `[-5,5]` window. The solution is the x-coordinate of the point of
intersection.
An alternative solution is to divide both sides of sides of the equation by cos x to get tanx=5. use your calculator to get `tan^(-1)5=1.373`. this is the first-quadrant solution, so add `pi`.
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