Find the measure of feta, to the nearest degree where o degrees is less than feta which is less than 360 degrees.
6 sin feta = -1
I really don't get how to solve, I hate algebra, and I feel that it's gonna be getting used in this question.
If you hate algebra, you're in for some bad times in trig!
6 sin feta = -1
sin feta = -1/6
Now, sin feta = y/h where h is the hypotenuse of a right triangle with base on the x-axis. h is always positive, so y must be negative.
That makes the angle in the 3rd or 4th quadrant.
Arcsin(1/6) = 9.6 deg
So, you will need to use 180+9.6 or 360-9.6
feta = 189.6 or 150.4 degrees.
While you can use whatever names you want for your angles, theta, a Greek letter is a more common name.
To find the measure of feta, we can use the inverse trigonometric function. In this case, since we have the equation 6 sin feta = -1, we can rearrange it to isolate the sine function by dividing both sides by 6:
sin feta = -1/6
Now, to find the angle whose sine is -1/6, we can use the inverse sine function or the arcsine function. The arcsine function is denoted as sin^(-1) or asin.
Let's use a scientific calculator to find the arcsine (-1/6). On most calculators, the arcsine function is represented as sin^(-1) or "sin inverse" or "asin."
1. Press the "sin^(-1)" or "asin" button on your calculator.
2. Enter -1/6 or -0.1666667 (approximately) followed by the "=" or "Enter" button.
The calculator should give you the result:
feta ≈ -9.58 degrees
However, since we are looking for the measure of feta between 0 and 360 degrees, we need to adjust this angle accordingly.
Since sin is negative in the third and fourth quadrants, we can add 180 degrees to get an angle in the fourth quadrant.
feta ≈ -9.58 + 180 degrees
feta ≈ 170.42 degrees
Therefore, to the nearest degree, feta ≈ 170 degrees.