Question

Find sin theta if theta is an angle in standard position and the point with coordinates (3, -4) lies on the terminal side of an angle.

Answer 1

A.

Explanation:

-4/5

Answer 2

`\sin \theta=-(4)/(5)`

Explanation:

Given:

Angle is in standard position which means the starting ray is at the origin. The terminal side has coordinates (3, -4).

So, the 'x' value is 3 and 'y' value id -4.

Using Pythagoras Theorem, we find the hypotenuse.

Hypotenuse =
`√(3^2+(-4)^2)=√(9+16)=√(25)=5`

Now, using the sine ratio for the angle, we have

`\sin \theta=(Opposite)/(Hypotenuse)\\\sin \theta=(-4)/(5)\\\sin \theta=-(4)/(5)`

Therefore, the value of
`\sin \theta` is
`-(4)/(5)`.

The value is negative as the point (3, -4) lies in the fourth quadrant and sine ratio is negative in the fourth quadrant,