solve sin theta = 1/2,90 degrees less than theta less than 180 degrees
To solve the equation sin(theta) = 1/2, where 90 degrees is less than theta and is less than 180 degrees, you can follow these steps:
Step 1: Recall the values of the sine function for special angles. The sin function is positive in the first and second quadrants, and its value is 1/2 at the angle 30 degrees or pi/6 in radians.
Step 2: Decide on the range of solutions based on the given condition. The condition states that the angle theta is greater than 90 degrees and less than 180 degrees.
Step 3: Determine the reference angle. To find the reference angle, subtract the angle given in the equation (30 degrees or pi/6 radians) from 180 degrees or pi radians. In this case, the reference angle is 180 degrees - 30 degrees = 150 degrees or pi - pi/6 = 5pi/6 radians.
Step 4: Determine the solutions in the specified range. Since sin function is positive in the first and second quadrants, consider the reference angle as a positive value and find the solutions.
First Solution: To get the first solution, add the reference angle (150 degrees or 5pi/6 radians) to 90 degrees. Therefore, theta = 90 degrees + 150 degrees = 240 degrees.
Second Solution: To get the second solution, subtract the reference angle (150 degrees or 5pi/6 radians) from 180 degrees. Therefore, theta = 180 degrees - 150 degrees = 30 degrees.
So, the solutions to sin(theta) = 1/2, where 90 degrees < theta < 180 degrees, are theta = 240 degrees and theta = 30 degrees.
make sure your calculator is set to degrees
2nd
sin
(1/2.9)
= 20.17
You want the angle between 0 and 180, that is in the I or II quadrant.
20.17° is in quadrant I
the angle in quadrant II would be 180 - 20.17 = 159.83°
check:
take the sine of each of those angles and compare it to 1/2.9