sin(π/2-x)
To simplify the expression sin(π/2 – x), we can use the trigonometric identity sin(π/2 – x) = cos(x)
To simplify the expression sin(π/2 – x), we can use the trigonometric identity sin(π/2 – x) = cos(x).
The trigonometric identity sin(π/2 – x) = cos(x) is derived from the fact that the sine function represents the y-coordinate of a point on the unit circle, while the cosine function represents the x-coordinate.
In this case, by subtracting x from π/2, we are shifting the angle x from the positive x-axis towards the positive y-axis. This results in a right triangle with an angle x and a hypotenuse of 1 (since we’re dealing with the unit circle).
So, sin(π/2 – x) is equal to the opposite side (which represents the y-coordinate) divided by the hypotenuse, which gives us sin(π/2 – x) = cos(x).
Therefore, sin(π/2 – x) simplifies to cos(x).
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