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

Question

In Exercises 85–96, use a calculator to solve each equation, correct to four decimal places, on the interval [0, 2𝝅).7 sin² x - 1 = 0

Accepted Answer

Hello, today we're going to be solving the following trigonometric equation with the help of a calculator. So what we are given is five sine squared of X minus three is equal to zero. And we only want the values of X within the range of 0 to pi not including two pi. Well, before you enter this value into a calculator, you'll first need to simplify the given equation. We need to get the value of sine by itself. And in order to do that, we're going to first add three to both sides of the equation that is going to leave us with five sine squared of X is equal to three. Next, we're going to divide both sides of the equation by five and that will leave us with sine squared of X is equal to 3/5. The next step in simplifying the equation is you want to eliminate the exponent of two. And in order to do that, we're going to take the square root of both sides of the equation. And that is going to leave us with sign of X is equal to the square root 3/5. Now, at this point here. The question is asking us what values of X can we plug into sine in order to get the value of square root 3/5. If you were to plug in this equation into a calculator, you'll end up with four values of X. But keep in mind that we only want to keep four decimal places of these values. So the first value of X rounded to four decimal places is going to be X is equal to 0.8861. The next value will be X is equal to 2.255. The next value will be X is equal to 4.276. And the final value of X is going to be given to us as 5.3971. These are going to be the four estimated values of X that will give a sign of X is equal to the square root 3/5. And with that being said, the answer to this problem is going to be a. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

In Exercises 85–96, use a calculator to solve each equation, correct to four decimal places, on the interval [0, 2𝝅).7 sin² x - 1 = 0

Key Concepts

Trigonometric Functions

Quadratic Equations

Interval Notation

Watch next