Solve Equation w/ Arcsin: How to Get 1/sqrt2 from pi/4

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In summary, the equation for solving for 1/sqrt2 from pi/4 using arcsin is 1/sqrt2 = arcsin(pi/4). The value of 1/sqrt2 is approximately 0.707107. To solve for 1/sqrt2 using the arcsin function, you need to convert pi/4 to radians and use the inverse sine function on your calculator. 1/sqrt2 is a common value in mathematics and has many applications. The specific method for getting 1/sqrt2 from pi/4 using the arcsin function is to input pi/4 (in radians) into the inverse sine function, resulting in an angle of pi/4 (equivalent to 45 degrees)
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Hello, I was trying to solve an equation with arcsin and I wasn´t sure about the result so I tried wolfram alpha with step by step solution and there is one step that I don´t understand, the one where you take the sine of both sides. How can I get 1/sqrt2 from pi/4 ? Thanks for help.View attachment 4961
 

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sin(pi/4) = 1/sqrt(2) is probably the most well-known trigonometric value (it comes from the isosceles right angle triangle).
 

FAQ: Solve Equation w/ Arcsin: How to Get 1/sqrt2 from pi/4

What is the equation for solving for 1/sqrt2 from pi/4 using arcsin?

The equation is 1/sqrt2 = arcsin(pi/4).

What is the value of 1/sqrt2?

The value of 1/sqrt2 is approximately 0.707107.

How do you solve for 1/sqrt2 using the arcsin function?

To solve for 1/sqrt2 using the arcsin function, you first need to convert pi/4 to radians by multiplying it by pi/180. Then, use the arcsin function on your calculator to find the angle that has a sine of 1/sqrt2. The resulting angle will be pi/4, which is equivalent to 45 degrees.

What is the significance of 1/sqrt2 in mathematics?

1/sqrt2 is a common value in mathematics and is often used in trigonometry and geometry. It is the ratio of the length of the hypotenuse to the length of one of the sides in a 45-45-90 degree triangle. It is also used in many other mathematical equations and has various applications in different fields of science.

Is there a specific method for getting 1/sqrt2 from pi/4 using the arcsin function?

Yes, the specific method is to use the inverse sine function (arcsin) on your calculator with an input of pi/4 (in radians). The resulting angle will be pi/4, which is equivalent to 45 degrees, and the sine of this angle is 1/sqrt2.

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