Question

Use a calculator to solve for 0 in the given interval.
sin0 = -0.9419, for pi<=0<=3pi/2

Answer 1

To solve for θ0 where sin(θ0) = -0.9419 in the interval π≤θ0≤3π/2, use the inverse sine function on a calculator and adjust the result to find the equivalent angle in the third quadrant.

Step-by-step explanation:

To solve for θ0 in the given interval where the sine of θ0 is equal to -0.9419, and the interval is π≤θ0≤3π/2, you can follow these steps:

1. On your calculator, enter the inverse sine function, often labeled as 'sin⁻¹' or 'asin'.
2. Input the value -0.9419 into the inverse sine function and execute the calculation.
3. The calculator might provide an angle in the fourth quadrant. Since we are interested in the interval π≤θ0≤3π/2, which corresponds to the third quadrant, we must find the equivalent angle in this quadrant. This is because the sine is also negative in the third quadrant.
4. To find the angle in the third quadrant, subtract the angle provided from π (3.14159) if the angle is less than π. If the angle provided is greater than π, then subtract the angle from 2π to get the correct value of θ0.

Make sure your calculator is set to the correct mode (degrees or radians) that is applicable to your question before performing the calculation.