Solve the equations to the nearest tenth and use the given restrictions.
2. sin theta = -0.204, for 90 degs < theta < 270 degs
Ans: 191.8 degs?
sin A = -0.204
A = -11.8o = 11.8o W. of S. = 258.2o CCW
from + X-axis.
Correction: If Sin A = -0.204
A = -11.8o = 11.8o N. of W. = 168.2o CCW
from + x-axis; Q2.
If Sin A = 0.204
A = 11.8o S. of W. = 191.8o CCW from +
x-axis.
To solve the equation sin(theta) = -0.204, you can use the inverse sine function (also known as arcsin or sin^(-1)). The inverse sine function will give you the angle whose sine is equal to a given value.
Here's how you can use the inverse sine function to solve this equation:
1. Start by setting up the equation:
sin(theta) = -0.204
2. Use the inverse sine function to isolate theta:
theta = sin^(-1)(-0.204)
3. Use a calculator with the inverse sine function to find the angle. Make sure your calculator is set to degrees mode.
Evaluating sin^(-1)(-0.204) on a calculator should give you approximately -11.8052 degrees.
4. Since the given restriction is 90 degrees < theta < 270 degrees, -11.8052 degrees is not within this range.
5. To find an angle within the given restriction that has the same sine value, you can subtract the angle from 180 degrees.
180 degrees - 11.8052 degrees = 168.1948 degrees
6. Round the answer to the nearest tenth:
168.2 degrees
Therefore, the approximate solution to the equation sin(theta) = -0.204, within the given restriction 90 degrees < theta < 270 degrees, is 168.2 degrees.