Determine two angels between 0 degrees and 360 degrees that have a sine ratio of -1/2. Would that be 30 and 330?
so you want sinØ = -1/2
Then angle must be in quadrants III or IV
then angle in standard position is 30° (because sin30° = +1/2)
so our angle is 180+30 = 210° in III
or our angle is 360-30 = 330 ° in IV
check by taking sin 210 and sin 330
To determine the angles between 0 degrees and 360 degrees that have a sine ratio of -1/2, we can use the inverse sine function (also known as arcsine) which is denoted as sin^(-1) or asin on most calculators.
The arcsine function gives us the angle whose sine equals the given ratio. In this case, we want to find the angles that have a sine ratio of -1/2.
To get the first angle, calculate the arcsine of -1/2:
asin(-1/2) ≈ -30.00 degrees
The arcsine function gives us the principal value, which means it only provides one angle in the range of -90 to 90 degrees. However, we can use the symmetry of the sine function to find the second angle.
The sine function is positive in both the first and second quadrants, so the second angle can be found by subtracting the first angle from 180 degrees:
180 degrees - (-30.00 degrees) = 210.00 degrees
Therefore, the two angles between 0 degrees and 360 degrees that have a sine ratio of -1/2 are approximately -30.00 degrees and 210.00 degrees.
Please note that the second angle you mentioned, 330 degrees, does not have a sine ratio of -1/2.