Write as a Function of x sin(x)=( square root of 2)/2

Problem

sin(x)=√(,2)/2

Solution

1. Identify the equation as a basic trigonometric equation where the sine of an unknown angle x is equal to a known value.

2. Determine the reference angle by finding the value in the first quadrant where the sine function equals √(,2)/2

3. Apply the knowledge of the unit circle, noting that sin(π/4)=√(,2)/2 or sin(45)=√(,2)/2

4. Find the second solution within the interval [0,2*π) by using the identity sin(π−θ)=sin(θ) which gives x=π−π/4=(3*π)/4

5. Generalize the solution to include all possible angles by adding multiples of the period 2*π where n is any integer.

Final Answer

x=π/4+2*n*π,(3*π)/4+2*n*π

Want more problems? Check here!