# Find Radians: How to Use Sin to Solve for X

• pooker
In summary, the conversation discusses finding the value of sin3x if sinx=1/3 and 0 < x < pi/2. The formula for the sine of the sum of two angles is needed, and the double-angle formulas for sin and cos are used to convert the expression. If the roles were reversed, the inverse of the cosine function is used to find the value of cosx. The restrictions on x must be taken into account when finding the value of cosx.
pooker
I do not need you to give me an answer just a formula

I have some problems to work and I cannot find anything through searching, I can make up a problem, but for example

find sin3x if sinx=1/3 and 0 < or equal to sin greater than or equal to pie/2

How would I find x? I now how to plug in a radian into my calculator to get the answer the opposite way but not this way.

Put your calculator down. You don't need it for any of this. If you want the exact answer, you don't need it at all.

You need the formula for the sine of the sum of two angles.
sin(3x) = sin(2x + x) = ??

You'll get an expression involving sin(2x), sin(x), cos(2x), and cos(x).

Convert the sin(2x) and cos(2x) factors by using the double-angle formulas for sin and cos.

After you have done all that, you should have an expression that involves only sinx and cosx. You're given that sinx = 1/3, and I believe you are given than 0 < x < pi/2 (not pie/2). If you know that sinx = 1/3 and that x is in the first quadrant, what must cosx be?

How would I find it if the roles were reversed, let's say

cos2theta = 1/3 and find costheta?

I understand the double angle formula, but I do not understand howto apply it in this case.

pooker said:
How would I find it if the roles were reversed, let's say

cos2theta = 1/3 and find costheta?

I understand the double angle formula, but I do not understand howto apply it in this case.

The double-angle formula doesn't apply here. Instead, you need to use the inverse of the cosine function.

Given that cos($2\theta$) = 1/3, then $2\theta$ = cos-1(1/3), so $\theta$ = 1/2 cos-1(1/3).

Hopefully there are some restrictions on $\theta$, but once you know it, you can determine cos($\theta$).

## 1. What is the relationship between sin, radians, and solving for x?

The sine function is commonly used to find the relationship between the sides and angles of a right triangle. When working with radians, the angle measure is represented by the length of the corresponding arc on the unit circle. Using the sine function, we can solve for x by finding the ratio of the opposite side to the hypotenuse of the triangle.

## 2. How do I convert from degrees to radians?

To convert from degrees to radians, you can use the formula: radians = (degrees * π) / 180. This means that to convert from degrees to radians, you multiply the degree measure by π and divide by 180. For example, to convert 45 degrees to radians, you would do (45 * π) / 180 = 0.7854 radians.

## 3. Can I use a calculator to find the sine of an angle in radians?

Yes, most scientific calculators have a function to calculate the sine of an angle, including angles in radians. Simply enter the angle in radians and press the sine button to get the result.

## 4. Are there any special cases when solving for x using sin and radians?

One special case is when the angle is equal to π/2 radians (or 90 degrees). In this case, the opposite side of the triangle is equal to the hypotenuse, making the sine ratio equal to 1. This means that x is equal to the length of the hypotenuse. Another special case is when the angle is equal to 0 radians (or 0 degrees). In this case, the opposite side is equal to 0, making the sine ratio also equal to 0, and x is equal to 0 as well.

## 5. How can I use the inverse sine function to solve for x?

The inverse sine function, also known as arcsine, is the opposite of the sine function. It is used to find the measure of an angle when given the ratio of the opposite side to the hypotenuse. To use the inverse sine function to solve for x, simply take the inverse sine of the ratio and convert the result from radians to degrees if necessary.

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