Solve each equation (x in radians and θ in degrees) for a...

Question

Solve each equation (x in radians and θ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures.

√2 sin 3x - 1 = 0

√2 sin 3x - 1 = 0

Accepted Answer

By all solutions of the given equation express your answer in radiance using the least possible nonne angle measure round your answer to the nearest 100th if necessary, where we have two sine five X plus the square root of three equals zero, we have four possible answers which are all angle measures. And we have a unit circle on the right side for helping with our angle. Now to solve this, let's first attempt to solve for X. So I will write out our equation. You can try this out, we can first move over our square root of three by subtracting both sides giving us two sine five X equals the negative square root of three. Now X is still inside of our sine function. So we need to get rid of our two. First, we'll divide both sides by two to get sin five X equals negative square roots of three divided by two. Now we need to get rid of our sign function. Since we have a sign function, we can get rid of it. By taking the inverse sine function, we get five X equals sine inverse of negative squared of three divided by two now, we can make use of our unit circle to find this result. We have sine inverse negative three divided by two, which corresponds to two angles on our unit circle. We need to find where are Y equals negative square roots of three divided by two. Looking at our inner circle, we see this happens in two places at the angle by pi divided by three and at the angle four pi divided by three. So we will write those on the side here. Since we have two different angles, we will split up our equation. We have five X equals 24 pi divided by three, N five X is equals 25 pi divided by three. Now, because of how sine works, we know Sine has the same value for every two pi cycle. We go around the circle. In other words, we need to add a two pie in to both angles. Now we have five X, let's divide both sides by five. To get our final equations. We get X equals four pi divided by 15 plus two pie in divided by five. And yet X equals pie divided by three plus two pi N divided by five. These are the two equations or our answer. We convince C the answer to our problem corresponds with answer A OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

Solve each equation (x in radians and θ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures.

√2 sin 3x - 1 = 0

Key Concepts

Solving Trigonometric Equations

Angle Measures and Unit Conversion

Using Inverse Trigonometric Functions and Periodicity

Watch next

Solve each equation (x in radians and θ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures.√2 sin 3x - 1 = 0

Key Concepts

Solving Trigonometric Equations

Angle Measures and Unit Conversion

Using Inverse Trigonometric Functions and Periodicity

Watch next