Question

9Let O be an angle in quadrant II such that csc =4"Find the exact values of tan 0 and cos 0.

Answer 1

Answer: cscθ = 4/√15, cot=-1/√15.

Step-by-step explanation:

For this question we will use the following diagram:

Using the Pythagorean theorem we know that:

`l^2+(-(1)/(4))^2=1^2.`

Solving for l we get:

`\begin{gathered} l^2=1-(1)/(16)=(15)/(16), \\ l=\frac{\sqrt[]{15}}{4}. \end{gathered}`

Therefore:

`\csc \theta=(1)/(l)=\frac{1}{\frac{\sqrt[]{15}}{4}}=\frac{4}{\sqrt[]{15}}.`
`\cot \theta=-((1)/(4))/(l)=-\frac{4}{4\sqrt[]{15}}=-\frac{1}{\sqrt[]{15}}.`