Question

What is the angle (t) if sqrt{65}/65" alt="sin(t)=4\sqrt{65}/65" align="absmiddle" class="latex-formula">. 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

Answer:

330.3 degrees

Step-by-step 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.