Question

Hello, I need help solving question 3 c . This is relating to trigonometric relationships between acute and obtuse angles (ASTC)

Answer 1

Using a calculator, let's calculate the angles that have these values of sin, cos and tan:

`\begin{gathered} a\text{.} \\ \sin (\theta)=0.8235 \\ \theta_1=55.44\degree \\ \theta_2=180-55.44=124.56\degree \\ \\ b\text{.} \\ \cos (\theta)=-0.5321 \\ \theta_1\colon\text{ doesn't exist, since cos is positive in first quadrant} \\ \theta_2=122.15\degree \\ \\ c\text{.} \\ \tan (\theta)=0.7685 \\ \theta_1=37.54\degree \\ \theta_2\colon\text{ doesn't exist, since tan is negative in second quadrant} \\ \\ d\text{.} \\ \tan (\theta)=-1.6328 \\ \theta_1\colon\text{ doesn't exist, since tan is positive in first quadrant} \\ \theta_2=121.49\degree \end{gathered}`