Question

What is the value of sinθ given that (3, −7) is a point on the terminal side of θ ? −758√58 758√58 358√58 −358√58?

Answer 1

Answer:

$\boxed{\sin(\theta)=-\frac{7}{58}\sqrt{58}}$

Step-by-step explanation

The given point $(3,-7)$ tells us that the terminal side of $\theta$ is in the fourth quadrant.

From the diagram in the attachment,

We can use the Pythagoras Theorem to find the length of the hypotenuse of the right triangle.

Let the hypotenuse be $h\: units$. Then,

$h^2=7^2+3^2$

$h^2=49+9$

$h^2=58$

$\Rightarrow h=\sqrt{58}$

Now we use the sine ratio;

$\sin(\theta)=\frac{Opposite}{Hypotenuse}$.

But since the terminal side of $\theta$ is in the fourth quadrant, the sine ratio must be negative.

This implies that;

$\sin(\theta)=-\frac{7}{\sqrt{58}}$.

We rationalize the denominator to get;

$\sin(\theta)=-\frac{7}{58}\sqrt{58}$.