Answer:
Just find sin^2theta and change them with the help of known identities.
You can also use Pythagoras theorm. It will work..
Hope it helps
Answer:
[tex]cos\theta=-\frac{1}{2}[/tex]
[tex]tan\theta=\sqrt3[/tex]
Step-by-step explanation:
We are given that
[tex]sin\theta=-\frac{\sqrt3}{2}[/tex]
Where [tex]\theta [/tex] lies between [tex]\pi\;and\;\frac{3\pi}{2}[/tex]
We have to find the value of [tex]cos\theta[/tex] and [tex]tan\theta [/tex]
[tex]\theta [/tex] lies in third quadrant
[tex]cos\theta=\sqrt{1-sin^2\theta}[/tex]
[tex]cos\theta=\sqrt{1-(\frac{\sqrt3}{2})^2}=\sqrt{1-\frac{3}{4}}=\sqrt{\frac{1}{4}}=\pm\frac{1}{2}[/tex]
[tex]cos\theta[/tex] is negative in third quadrant
Therefore, [tex]cos\theta=-\frac{1}{2}[/tex]
[tex]tan\theta=\frac{sin\theta}{cos\theta}=\frac{\frac{-\sqrt3}{2}}{\frac{-1}{2}}[/tex]
[tex]tan\theta=\frac{\sqrt3}{2}\times 2[/tex]
[tex]tan\theta=\sqrt3[/tex]
[tex]tan\theta[/tex] is positive in third quadrant
Hence, [tex]tan\theta=\sqrt3[/tex]
