Find a value of θ in the interval [0°, 90°) that satisfies each s...

Question

Find a value of θ in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. See Example 2.

sin θ = 0.84802194

Accepted Answer

Welcome back. Everyone. In this problem, we want to determine the value of theater that satisfies the equation sine theta equals 0.46973597. We want to consider only a value that is in the interval, open bracket, zero degrees, 90 degrees closed parentheses. And we want to express our answer in decimal degrees rounded to six decimal places for our answer choices. A is 26. degrees. B is 32. degrees. C is 19. degrees and the D is 28.017159 degrees. Now, what do we know here? Well, we know that the sign of theta equals 0.46973597. So if we need to, if we're going to figure out the, then what can help us is the sign inverse because recall that if we have an angle theta and we apply the sine function to figure out its ratio, then we can take that ratio and find the inverse sign function to give us back the angle that we started with. And that's exactly what we want to do here. So that tells us then that theta would be equal to the inverse sign of our ratio, which is 0.46973597. Now using a calculator, you get the approximate value for the inverse sign of our number to be 28. degrees. In other words, the sign of this angle would give us our ratio. But remember we want to express our answers around it to six decimal places. So that means if we look in our number, the sixth decimal place is at nine, the place value beside it is one. And since it's less than five, we would not need to round up. Therefore, round it to six decimal places, theta equals 28.017159 degrees. And when we look in our answer choices, that would have been answer choice. D Thanks a lot for watching everyone. I hope this video helped.

Find a value of θ in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. See Example 2. sin θ = 0.84802194

Key Concepts

Sine Function

Inverse Sine Function

Angle Measurement in Degrees

Watch next