I need a little help

That is a really good answer Will85237

I'll show you another approach :)
     

If sine of Theta=0.4, what is the value of cosine of Theta?

 

0.4= 2/5

 

Draw a right angled triangle and label one of the acute angles as theta.

sine theta = 2/5

so mark the opposite side as 2 and the hypotenuse as 5

The adjacent side will be sqrt(25-4) = sqrt(21)

 

So cos(theta) = sqrt(21)/5 = sqrt(0.84)    which is exactly what Will found.

 

Theta could also be  in  the 2nd quadrant. In this case cos(theta) = -sqrt(21)/5 

Use the following trigonometric identity.

\(sin^2(\theta )+cos^2(\theta )=1 \)

Rearrange it in terms of cos.

\(cos(\theta )=\sqrt{1-sin^2(\theta )}\)

Substitute in your value of sine of theta, 0.4.

\(cos(\theta )=\sqrt{1-0.4^2}\)

Solve.

\(cos(\theta )=\sqrt{1-0.16}\)

\(cos(\theta )=\sqrt{0.84}\)

As an approximation.

\(cos(\theta )=0.92\)