Thread: Trigonometry Equations? multiples of pi?

how would i go about solving this question?

Solve the following equations in the interval [0, 2pi]. Give the answer as a multiple of pi. Do not use decimal numbers. The answer should be a fraction or an integer.

sin(t) = -(sqrt(3))/2
t = __?__ pi

sin(t) = -1/2
t = __?__ pi

Do you know the unit circle?

Solve for the basic angle , where all solutions are positive, then use symmetry to evaluate the negative answers - sine is negative in the 3rd and 4th quadrants.

Basic angle(B) = arcsin(sqrt3/2)
When you have derived the basic angle, check the quadrants in which sin is negative( 3rd and 4th) and hence the solutions are pi+ B and 2pi - B

Do the same for the 2nd question.
You may want to draw the quadrants to help you visualise and understand the problem better.

Hope this helps.