Solve Sin pi/12= 1/4 (√6 - √2)

Thread starter CrossFit415
Start date Mar 27, 2011
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Sin

In summary, the equation "Sin pi/12= 1/4 (√6 - √2)" is asking to solve for the value of x that satisfies the equation Sin x = 1/4 (√6 - √2). The value of pi/12 in degrees is approximately 15 degrees. To solve for x, we can use trigonometric identities and algebraic manipulations. Simplifying the equation before solving for x helps to reduce complexity and make the solution process more efficient. Other methods to solve this equation include using a calculator or software program, as well as using the unit circle, but using trigonometric identities is the most efficient and reliable method.

Mar 27, 2011

CrossFit415

Sin pi/12= 1/4 (√6 - √2) ?

I took sin pi/12 = sin (4pi / 12 - 3pi/12) = sin (pi/3 - pi/4)

Did I do this right?

Last edited: Mar 27, 2011

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Mar 27, 2011

Dick

Science Advisor

Homework Helper

And then used the difference formula? The answer looks ok to me.

Mar 27, 2011

CrossFit415

Yea I did

Mar 27, 2011

Dick

Science Advisor

Homework Helper

You can, of course, just put sin(pi/12) into your calculator and check that it matches 1/4 (√6 - √2), if you want to check yourself.

Mar 27, 2011

CrossFit415

Thanks

FAQ: Solve Sin pi/12= 1/4 (√6 - √2)

What is the equation "Sin pi/12= 1/4 (√6 - √2)" asking to solve?

The equation is asking to solve for the value of x that satisfies the equation Sin x = 1/4 (√6 - √2).

What is the value of pi/12 in degrees?

The value of pi/12 in degrees is approximately 15 degrees.

How do you solve for x in this equation?

To solve for x, we can use trigonometric identities and algebraic manipulations. First, we can simplify the right side of the equation by combining the square root terms and dividing by 4. Then, using the sine of a difference identity, we can express the left side as Sin(pi/6)Cos(pi/12) - Cos(pi/6)Sin(pi/12). Finally, using the values of Sin(pi/6) = 1/2 and Cos(pi/6) = √3/2, we can solve for x.

Why is it important to simplify the equation before solving for x?

Simplifying the equation helps to reduce the complexity of the problem and makes it easier to identify the appropriate trigonometric identities to use. It also makes the solution process more efficient.

Are there any other methods to solve this equation?

Yes, there are other methods such as using a calculator or software program to find the approximate value of x, or using the unit circle to find the exact value of x. However, using trigonometric identities and algebraic manipulations is the most efficient and reliable method to solve this equation.