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Ulleksa [173]
3 years ago
10

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.

Mathematics
1 answer:
alisha [4.7K]3 years ago
4 0

Answer:

\sin \theta=-\frac{4}{5}

Step-by-step 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 = \sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5

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

\sin \theta=\frac{Opposite}{Hypotenuse}\\\sin \theta=\frac{-4}{5}\\\sin \theta=-\frac{4}{5}

Therefore, the value of \sin \theta is -\frac{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,

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