Question

If sec theta = - √30 / 3, find cos theta.
if sin(-theta) = -0.97, find cos (π/2 - theta).

Answer 1

Explanation:

`\cos \theta = (1)/( \sec\theta ) = - (3)/( √(30) ) = - (3 √(30) )/(30) = - ( √(30) )/(10)`

`\cos( (\pi)/(2) - \theta )= \cos (\pi)/(2) \cos \theta + \sin (\pi)/(2) \sin \theta`

Note that

`\sin( - \theta) = - \sin \theta`

`\cos (\pi)/(2) = 0 \: \: \: \: \: \sin (\pi)/(2) = 1`

Therefore,

`\cos( (\pi)/(2) - \theta ) = 0.97`