How to find cos theta?

You'll just have to use a calculator   to find   cos (-3/2 degrees) = .999657

 

 

or if you need   cos ( -3/2 radians) = .070737

\(tan \theta = -\frac{3}{2}\\ \)

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Think about   \(tan \theta = +\frac{3}{2} \)    first

Draw a right angled triangle.

Mark an acute angle as theta.

opp = 3

adj=2

so hypotenuse  =     \(\sqrt{9+4}=\sqrt{13} \)

 

So for this triangle   \(cos\theta= \frac{2}{\sqrt{13}}=\frac{2\sqrt{13}}{13}\)

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Now, tan is negative in the 2nd and 4th quadrant

In the 2nd quad Cos is negative and in the 4th quad Cos is positive.

So

 

\(cos\theta=\pm\frac{2\sqrt{13}}{13}\)