Question

30 POINTS!! PLS SHOW WORK!!

Answer 1

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

Explanation:

Refer to the graph.

From the graph, we can see that our angle is in QII.

In QII, sine is positive and cosine and tangent are negative.

Since our point is at (-3, 4), this means that our adjacent side to our angle is -3 while our opposite side to our angle is 4.

To find sine, we need to find the hypotenuse c.

So, we can use the Pythagorean Theorem:

`a^2+b^2=c^2`

Substitute -3 for a and 4 for b. This yields:

`(-3)^2+(4)^2=c^2`

Square:

`9+16=c^2`

Add:

`25=c^2`

Take the square root of both sides:

`c=5`

So, our hypotenuse is 5.

And our adjacent is -3 and opposite is 4.

Now, remember that:

`\sin(\theta)=\text{opp}/\text{hyp}`

Substitute 4 for the opposite and 5 for our hypotenuse. This gives us:

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

Since sine is positive in QII, we don't need to add any negatives.

And we're done!