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

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.

tan θ = 6.4358841

Accepted Answer

Welcome back. Everyone. In this problem, we want to determine the value of theater that satisfies the equation. 10 theater equals 5.3281955. And we're considering 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 62.943852 degrees. B is 79. degrees. C is 73. degrees and D is 84.977582 degrees. So what do we want to know here? Well, we know that the tangent of theta is 5.3281955. In other words, that's the ratio when we find a tangent of our angle. Nor recall that if we have the tangent of theater being equal to a ratio, then our angle would be equal to the inverse tangent of that ratio. And that makes sense because the tangent is a function. And when we find the tangent of an angle, we're applying a function to get a ratio or a value. So if we want to find the angle from which that ratio comes, then we would do the opposite. In other words, we would do the inverse tangent. And that's the idea that we need to apply here. So since the tangent of theta equals this ratio, that means theta equals to the inverse tangent of 5.3281955. Now, using our calculator, we'll find that theta is approximately equal to 79.370. Let me write that properly 33773 degrees. But remember we only want our answer rounded to six decimal places. When we look in our number, our sixth decimal place has the digi digit seven beside it, the number is greater than five. So that means we would round up. Therefore, theta is approximately equal to 79. degrees rounded to six decimal places. When we look in our answer choices that would have been answer choice. B 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.
tan θ = 6.4358841

Key Concepts

Tangent Function

Inverse Tangent (Arctan) Function

Angle Measurement and Interval Restrictions

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