Question

The terminal side of an angle Ø in standard position is 6 quadrant 4. If cosØ=0.6, find sinØ.

Answer 1

From the question, the terminal angle is in quadrant 4

`\begin{gathered} cos\theta=0.6 \\ cos\theta=(adjacent)/(hypotenuse)=(6)/(10) \end{gathered}`

Let's find the opposite side. from Pythagoras, we have

`\begin{gathered} hyp^2=opp^2+adj^2 \\ 10^2=opp^2+6^2 \\ 100=opp^2+36 \\ opp^2=100-36 \\ opp^2=64 \\ opp=√(64)=8 \end{gathered}`

So,

`\begin{gathered} sin\theta=(opposite)/(hypotenuse) \\ sin\theta=(8)/(10)=0.8 \end{gathered}`

In the 4th quadrant, only cos is positive. So, sine is negative

Hence the answer is

`sin\theta=-0.8`

Option D is the answer