This is for trigonometry.
A searchlight rotates through one complete revolution every 20 seconds. How long does it take the light to rotate through 90 degrees? Please help me set up and solve the problem. Thanks!

Question

This is for trigonometry. 
A searchlight rotates through one complete revolution every 20 seconds. How long does it take the light to rotate through 90 degrees? Please help me set up and solve the problem. Thanks!

istim · Answer

IS 90 degrees the period?

anonymous · Answer

Remember that one full rotation is 360 degrees. For every 360 degrees of rotation, 20 seconds pass in time. Now, if it rotates 90 degrees, then how much of a rotation is that? Well let's ask that mathematically
90 = x*360
Solve for x and you get that 90 degrees is 1/4 of a rotation.
So, if it rotates 1/4 of a revolution, it will take 1/4 of the time.

anonymous · Answer

Thank you pstlwhppd! That made a lot of sense. I did not think about it that way. Thanks for your help. I appreciate it.