Question

If sin theta = - squrt.3/2 and pi < theta < 3pi/2, what are the values of cos theta and tan theta?

Answer 1

Answer with explanation:

Let, A=Theta

→Used the identity

Sin²A+Cos²A=1

→Sine and cosine are negative in third Quadrant.

$\sin A= \frac{-\sqrt{3}}{2}\\\\\pi < A$

Answer 2

So this first wants you to find where sin is √3/2 when θ is between π and 3π/2. θ would therefore be located at 2π/3.

Now plug in the value of θ for cosine:

cos (2π/3) = -1/2

And tangent:

tan (2π/3) = -√3/3