Question

5 cos theta + 12 sin theta = 13 then find the Value of sin theta

Answer 1

I am using x in case of theta-------------->

so 5 cosx = 13-12 sinx

squaring on both sides we get,

25 cos²x = 169 + 144 sin²x - 312 sinx

in case of cos²x we substitute (1-sin²x), as sin²x + cos²x = 1

equation will be 169 sin²x - 312 sinx + 144 = 0

after using quadratic formula we get sinx = 312/338

so sinx = 12/13.

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Answer 2

Answer

Step-by-step explanation:

so 5 cosx = 13-12 sinx

squaring on both sides we get,

25 cos²x = 169 + 144 sin²x - 312 sinx

in case of cos²x we substitute (1-sin²x), as sin²x + cos²x = 1

equation will be 169 sin²x - 312 sinx + 144 = 0

after using quadratic formula we get sinx = 312/338

so sinx = 12/13.