Question

if cos theta = negative square root 3 over 2 and pi < theta < 3pi over 2, what are the values of sin theta and tan theta?

Answer 1

we know that

`cos\theta=-(√(3))/(2)`

and the domain of angle θ is the interval

`(pi,(3pi)/(2))`

that means

The angle θ lies on the III quadrant

the value of sine is negative

the value of the tangent is positive

`\begin{gathered} x=cos^(-1)((√(3))/(2)) \\ x=30\text{ degrees} \end{gathered}`

the angle theta is equal to

θ=180+30=210 degrees=7pi/6 radians

see the figure below to better understand

Find out the value of sin

sinθ=-sinx=-sin30=-1/2

Find out the value of tanθ

tanθ=tanx

`tanθ=tanx=((1)/(2))/((√(3))/(2))=(1)/(√(3))=(√(3))/(3)`