Question

Use the given function value and the trigonometric identities to find the exact value of each indicated trigonometric function. (I already have the csc I need the others)

Answer 1

b.

In order to calculate the cotangent of 60°, we can use the relation below:

`\cot (90\degree-x)=(1)/(\cot x)=(1)/((1)/(\tan x))=\tan x`

So we have:

`\begin{gathered} \cot (90\degree-30\degree)=(1)/(\cot (30\degree)) \\ \cot (60\degree)=(1)/((1)/(\tan30\degree))=\tan 30\degree \\ \cot (60\degree)=\frac{\sqrt[]{3}}{3} \end{gathered}`

c.

To calculate the cosine of 30°, we can use the relation below:

`\tan x=(\sin x)/(\cos x)`

So we have:

`\begin{gathered} \tan 30=(\sin 30)/(\cos 30) \\ \frac{\sqrt[]{3}}{3}=((1)/(2))/(\cos 30) \\ \sqrt[]{3}\cos 30=(3)/(2) \\ \cos 30=\frac{3}{2\sqrt[]{3}}=\frac{\sqrt[]{3}}{2} \end{gathered}`

d.

Calculating the cotangent of 30°, we have:

`\cot (30\degree)=(1)/(\tan(30\degree))=\frac{1}{\frac{\sqrt[]{3}}{3}}=\frac{3}{\sqrt[]{3}}=\sqrt[]{3}`