In Exercises 85–96, use a calculator to solve each equation, c...

Question

In Exercises 85–96, use a calculator to solve each equation, correct to four decimal places, on the interval [0, 2𝝅). sin x = 0.8246

Accepted Answer

Hello, everyone. We are asked to solve the following trigonometric equation on the interval 0 to 2 pi including zero with the help of a calculator, we will round our final answer to four decimal places. The equation is the sign of X equals 0.6537. Our answer choices are a 0.7126 and 2.4292 B 0.7125 and 2.4292 C 1.7126 and 2.4292 D 0.7125 and 2.4291. OK. So going back to our equation, the sign of X equals 0.6537. So here, the first thing I'm noting is that sign is positive and if sin is positive, this means that the angle we are looking for must be in quadrant one in quadrant two because that is where sign is positive. So we are gonna have two values because this value could come from two different angles depending on which quadrant we are in. So to find the first value I'm gonna take the arc sign of 0.6537. I will put this in a calculator, make sure that your calculator is in radiance mode and we get 0.712463. Since we want this rounded to four decimal places, we're gonna round it to the number four and that will be rounded up. So one of our angles is 0.7125. So this is would be the angle in the first quadrant. So I'm just gonna draw an arbitrary line and the distance here would be 0.7125. The angle that would match that in the second quadrant would have a distance from the X axis to the angle of 0.7125. But we need to find the distance from standard position to that line. Knowing that the distance from the positive side of the X axis to the negative side of the X axis is pi I can find this angle by doing pi minus 0.7125. So I'm gonna take the pi distance from the standard position all the way to the other side of the X axis and subtract a reference angle of 0.7125. And when I do so, we are left with 2. 291. And since I rounded my first value to four decimal places, this one already is rounded to four decimal places. And this is our second angle measure. And now checking my answer choices, those are very similar, but the ones that have 0.7125 or B and D and D matches with our second angle. Also the 2.4291. So this is answer choice. D have a nice day.

In Exercises 85–96, use a calculator to solve each equation, correct to four decimal places, on the interval [0, 2𝝅). sin x = 0.8246

Key Concepts

Solving Trigonometric Equations

Using the Inverse Sine Function

Interval and Periodicity of Sine Function

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