Answer: [tex]x = \frac{\pi}{4} \ \text{radians}, \ \ y = \frac{\sqrt{2}}{2}[/tex]
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 [tex]\frac{\sqrt{2}}{2}[/tex]
You could also use your calculator to graph y = sin(x)-cos(x) to find the x intercept in the interval [tex]0 < x < \frac{\pi}{2}[/tex] to find the approximate x intercept to be x = 0.70710678
Then note how [tex]\frac{\sqrt{2}}{2} \approx 0.70710678[/tex]
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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.
