SOLUTION: if tan theta=3/2 and 90<theta<360 calculate without using a calculator the value of Sin2theta

Algebra ->  Trigonometry-basics -> SOLUTION: if tan theta=3/2 and 90<theta<360 calculate without using a calculator the value of Sin2theta       Log On


   

Question 1025259: if tan theta=3/2 and 90
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
tan%28theta%29=y%2Fx=%28y%2Fr%29%2F%28x%2Fr%29
So since the quotient is positive, x and y must have same sign,
y%2Fr=-3%2Fsqrt%282%5E2%2B3%5E2%29
x%2Fr=-2%2Fsqrt%2813%29
and
r=sqrt%2813%29
x=-2
y=-3
So then,
sin%28theta%29=y%2Fr
sin%5E2%28theta%29=y%5E2%2Fr%5E2
sin%5E2%28theta%29=9%2F13