Question

If sin(0)-iz, and 0 is in Quadrant IV, then what is tanº)?513

Answer 1

From the question,

We are given

`\sin \theta=-(5)/(13)`

And we are given that θ is in quadrant IV

We are to find

`\tan ((\theta)/(2))`

Since Sinθ is in quadrant IV then we have the diagram below

By applying Pythagoreans theorem

`(\text{hyp)}^2=(\text{opp)}^2+(\text{adj)}^2`

Then we have

`13^2=5^2+x^2`

Solving for x, we get

`\begin{gathered} x^2=13^2-5^2 \\ x^2=169-25 \\ x=\sqrt[]{144} \\ x=12 \end{gathered}`

Therefore, x = 12

From the question, we are to find tan(θ/2)

This will be done using the formula

`\tan ((\theta)/(2))=(\sin \theta)/(1+\cos \theta)`

Therefore, by applyingthe trigonometrical ratio

SOH CAH TOA

This gives