Question

if sin (theta) = -3/4 and cos (theta) >0, find the value of cos (theta)?

Answer 1

draw a triangle

Answer 2

there is a triangle with the opposite over the hypotenuse is \(\frac{3}{4}\)
all you need is the third side which you find via pythagoras

Answer 3

it is
\[x=\sqrt{4^2-9^2}=\sqrt{16-9}=\sqrt7\]

Answer 4

now you can take any trig ratio you like
this makes
\[\cos(x)=\frac{\sqrt7}{4}\]