Question

Evaluate

a) sin (alpha), given that sec (alpha)= -3, and that alpha is an obtuse angle.

b) cot(beta), given that tan(beta)=1/(√2) and that beta is an acute angle.

Answer 1

a) $90\degree<\alpha<180\degree$

$$\cos \alpha=\dfrac{1}{\sec \alpha}=-\dfrac{1}{3}$$

$$\sin \alpha=\sqrt{1-\cos^2 \alpha}=\sqrt{1-(-\dfrac{1}{3})^2}=\dfrac{2\sqrt{2}}{3}$$

b) $0\degree<\alpha<90\degree$

$$\cot \beta=\dfrac{1}{\tan \beta}=\sqrt{2}$$