Question

Some trig questions

Answer 1

2. Given tanθ = 8, find csc(θ).

Answer 2

\[\tan\theta=8~~\implies~~\tan^2\theta=64=\sec^2\theta-1\]
\[\sec^2\theta-1=\tan^2\theta~~\implies~~1-\cos^2\theta=\sin^2\theta~~\implies~~\csc^2\theta-\cot^2\theta=1\]
We know that \(\tan\theta=\dfrac{1}{\cot\theta}\), which means \(\cot\theta=\dfrac{1}{8}\), or \(\cot^2\theta=\dfrac{1}{64}\).

See where this is going?

Answer 3

Something to keep in mind: If \(\tan\theta=\dfrac{\sin\theta}{\cos\theta}>0\), this means either both \(\sin\theta\) and \(\cos\theta\) are positive, or both are negative. There are two cases to consider.