Question

For the problem below, find the reference angle, to the nearest 10th (if necessary), and also the two possible quadrants in which θ could lie.tan(θ)=−3

Answer 1

`\begin{gathered} \text{Tan}\theta=-3 \\ \theta=\tan ^(-1)-3 \\ \theta=-71.565^0 \\ \text{Tan is only negative on the second and fourth quadrant} \\ \text{Therefore for the second quadrant 180}^0-71.565^0\text{ }=108.435^0\approx108.4^0\text{nearest 10th} \\ \text{for the fourth quadrant 360}^0-71.565^0=288.435^0\approx288.4^0\text{nearest 10th} \\ \end{gathered}`

The two possible quadrants are the second and the fourth