Question

If $\sin \theta =\frac{1}{2}$ and $\cos \theta =-\frac{\sqrt{3}}{2}$, find the values of the other 4 trignometric functions.

Answer 1

• Given $\sin \theta =\frac{1}{2}$ and $\cos \theta =-\frac{\sqrt{3}}{2}$
• Which implies $\tan \theta =\frac{\sin \theta }{\cos \theta }=\frac{\frac{1}{2}}{-\frac{\sqrt{3}}{2}}=-\frac{1}{\sqrt{3}}$
• $\cot \theta =\frac{1}{\tan \theta }=-\sqrt{3}$
• $\sec \theta =\frac{1}{\cos \theta }=-\frac{2}{\sqrt{3}}$
• $\text{cosec}\theta =\frac{1}{\sin \theta }=2$