Question

If tan theta=3/4, find sin theta

Answer 1

sin(theta)=3/5

Explanation:

tan(theta)=3/4

sec^2(theta)=1+tan^2(theta)=1+(3/4)^2=1+9/16=(16+9)/16=25/16

sec(theta)=square root of(25/16)=5/4

sec(theta)=1/cos(theta)=5/4

cos(theta)=4/5

sin^2(theta)=1-cos^2(theta)=1–16/25=(25–16)/25=9/25

sin(theta)=3/5

So

sec(theta)=5/4

sin(theta)=3/5