Question

I have to solve for x how do I do this

Answer 1

Answer:
`x = (\pi)/(4) \ \text{radians}, \ \ y = (√(2))/(2)`

Note: pi/4 radians is equal to 45 degrees

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To get this answer, you can use the unit circle to see that at 45 degrees or pi/4 radians, the sine and cosine value are both
`(√(2))/(2)`

You could also use your calculator to graph y = sin(x)-cos(x) to find the x intercept in the interval
`0 < x < (\pi)/(2)` to find the approximate x intercept to be x = 0.70710678

Then note how
`(√(2))/(2) \approx 0.70710678`

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Or you could do the following steps

sin(x) = cos(x)

sin^2(x) = cos^2(x)

sin^2(x) = 1 - sin^2(x)

sin^2(x) + sin^2(x) = 1

2sin^2(x) = 1

sin^2(x) = 1/2

sin(x) = sqrt(1/2)

sin(x) = sqrt(2)/2

Again you'll have to turn to the unit circle, or some reference sheet, to determine the x value that makes the last equation above to be true. That x value is x = pi/4 radians.