If tan theta=3/4, find sin theta

sin (theta) = 3/5

Step-by-step 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