Question

Using the identity 2θ+2θ=1sin 2 θ+cos 2 θ=1, find the value of tanθtanθ, to the nearest hundredth, if cosθ=0.42cosθ=0.42 and 3π2<θ<2π23π <θ<2π.

Answer 1

we know that

The angle theta lies on the IV quadrant

that means ----> the sine and the tangent are negative

so

step 1

Find out the value of the sine

`sin^2\theta+cos^2\theta\text{=1}`

substitute given value

`\begin{gathered} s\imaginaryI n^2\theta+(0.42)^2=1 \\ s\imaginaryI n^2\theta=1-0.42^2 \\ s\imaginaryI n\theta=-0.91 \end{gathered}`

step 2

Find out the value of the tangent

`\begin{gathered} tan\theta=(sin\theta)/(cos\theta) \\ \\ tan\theta=-(0.91)/(0.42) \\ \\ tan\theta=-2.16 \end{gathered}`

The answer is -2.16