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
[tex]sin^2\theta+cos^2\theta\text{=1}[/tex]
substitute given value
[tex]\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}[/tex]
step 2
Find out the value of the tangent
[tex]\begin{gathered} tan\theta=\frac{sin\theta}{cos\theta} \\ \\ tan\theta=-\frac{0.91}{0.42} \\ \\ tan\theta=-2.16 \end{gathered}[/tex]
The answer is -2.16
