Question

5Cos$\theta$ + 12sin$\theta$ = 13.

Find sin$\theta$​

Answer 1

Answer:-

sin theta = 12/13

cos theta:- 5/13

Step-by-step explanation:

we have given,

5 cos theta + 12sin theta = 13

12 sin theta = 13- 5cos theta

take square on both sides

144 sin^2 theta = 169 - 25cos^2 theta

we know that ,

1 - sin^2 theta = cos^2 theta

144 - 144cos^2 theta = 169 - 130cos theta+ 25cos^2 theta

therefore,

0 = 25 -130cos theta + 169 cos^2 theta

0 = 25-65cos theta-65cos theta+169cos^2 theta

0=5(5-13cos theta)-13cos theta(5-13cos theta)

therefore ,

0= 5-13cos theta

5=13cos theta

therefore,

cos theta = 5/13

so sin theta =12/13