Question

What is the angle (t) if
`sin(t)=4√(65)/65`. Recall that theta lies in quadrant IV. The answer to this is 330.3 degrees, but please show how that answer is found.

Answer 1

330.3 degrees

Explanation:

sin t = 4√65 / 65 reduces to sin t = 4 / √65. As the sine function is defined as (opp side) / (hypotenuse), we see that opp side = 4 and hyp = √65 must be true. But sin t is positive in Quadrants I and II, not in Quadrant IV.

I will take the liberty of assuming you meant sin t = -4 / √65.

Then (opp side) = -4 and (hyp) = √65.

Use the inverse sine function on a calculator to determine this angle t:

-arcsin(4/√65) comes to -arcsin 0.4961 = -0.5191 radians.

Converting -0.5191 radians to degree measure results in

t = 360° - 29.745°, or 330.2551 degrees. This rounds off to 330.3 degrees.