if sin(x)=-0.5 and x is in the third quadrant, find x
a sine value of .5 means a 30º reference angle
in Q III, the angle is
... 180º + 30º = x
How did you find the answer exactly?
I am confused.
To find the value of x when sin(x) = -0.5 and x is in the third quadrant, we can use the following steps:
Step 1: Determine the related acute angle
Since the sine function is negative in the third quadrant, we can find the related acute angle by taking the inverse sine of the absolute value of -0.5.
sin^(-1)(0.5) ≈ 30°
Step 2: Find the angle in the third quadrant
In the third quadrant, the angle will be greater than 180° but less than 270°. To find the angle, subtract the related acute angle from 180°.
180° - 30° = 150°
Therefore, x is approximately 150° in the third quadrant.
To find the value of x when sin(x) = -0.5 in the third quadrant, we can use the fact that sine is negative in the third quadrant.
First, find the reference angle by calculating the inverse sine of 0.5:
sin^(-1)(0.5) ≈ 30°
Since we are in the third quadrant, the angle will be 180° + the reference angle:
x = 180° + 30° = 210°
Therefore, x is approximately equal to 210° in the third quadrant.