Question

find the exact value of cos(a+b) given that sin(a) = -1/2 with angle a in quadrant 4, and sin(b) = 1/4, with angle b in quadrant 2

Answer 1

The exact value of cos (a + b ) is - 15.53°

Explanation:

Given as :

sin (a) = -
`(1)/(2)`

sin (b) =
`(1)/(4)`

So, a = sin^{-1}(\frac{-1}{2})

i.e a = -30°

And b = sin^{-1}(\frac{1}{4})

I.e b = 14.47°

Now, cos (a + b ) = cos (-30° + 14.47° )

Or, cos (a + b ) = - 15.53°

Hence The exact value of cos (a + b ) is - 15.53° Answer