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√3 sin x/2 = 3

2√3 sin x/2 = 3

Accepted Answer

Find all solutions of the given equation express your answer and radiance using the least possible negative angle measure round your answer to the nearest 100th if necessary, where we have two squares of two sine X divided by four equals two. And we have four possible answers. And every answer has a pair of angle measures. And finally, we have a unit circle on the right of our screen. Now to solve this, let's try and find X, we have two squares of two sine X divided by four equals two. And our first step should be to divide both sides by two square roots of two. This will give us sin of X divided by four on one side and two divided by two squares of two on the other. Now, we can do a quick simplification, two divided by two squares of two equals one divided by the square root of two because our twos will cancel. Now we need to get rid of the radical and the denominator by multiplying by square root of two divided by the square root of two. This simplifies to the square root of two divided by two which we can now set equivalent to our sine X divided by four. Now we have square root of two divided by two and we have s on the left side, let's find the sine of some angle that equals square root of two divided by two with the unit circle. In other words, we need to find where the Y coordinate is equal to squared of two divided by two. We can see two places where that happens on the inner circle at the angle pi divided by four and at three pi divided by four. In other words, Sine of pi divided by four or sine of three pi divided by four equals the square root of two divided by two. Now we can split up our equation into two different equations. We get sine of X divided by four equals. So I divided by four and sine X divided by four equals sine three pi divided by four. We can then lose the signs on both sides to get X divided by four equals pi divided by four and X divided by four equals three pi divided by four. Now something else to notice is that for every loop around the circle, we reach the same angle measure and this happens every two pi radiance. So for both of our angles, we will add two pi multiplied by N and then we can solve for X multiplying or on both sides gives us X equals pi plus eight PN NX equals three pi multiplied by four, divided by four, which is just three pi plus once again eight pie in, we don't have anything else to simplify. So if we look at our possible answers, we can determine our answers of pi plus eight pi N and three pi plus eight pi N correspond to answer B 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√3 sin x/2 = 3

Key Concepts

Solving Trigonometric Equations

Unit Circle and Angle Measures

General Solutions for Sine Equations

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√3 sin x/2 = 3

Key Concepts

Solving Trigonometric Equations

Unit Circle and Angle Measures

General Solutions for Sine Equations

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√3 sin x/2 = 3