Question

The terminal side of an angle Ø in standard position is in quadrant 2. If cosØ = -0.5, find sinØ

Answer 1

Answer: C. 0.87

Step-by-step explanation

The signs of the function are dependent on the quadrant. In the image below, there is the sign of each function depending on the quadrant.

Then, as we are said that we are in quadrant II, it means that cosine is negative as we are given:

`\cos\theta=-0.5`

To get sin θ we have to solve for θ in the expression above:

`\cos^(-1)(\cos\theta)=\cos^(-1)(-0.5)`

Simplifying we get:

`\theta=120\degree`

Finally, we replace this value in the sine function:

`\sin(120\degree)=(√(3))/(2)\approx0.87`