Solution assignment 05 Unit circle and simple formulas

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Assignment 5

Show using the unit circle:

\cos(\displaystyle\frac{\pi}{2}+x)=-\sin(x)

Solution

Draw in the unit circle the angle x and next the angle:

\displaystyle\frac{\pi}{2}+x

The projection on the horizontal X-as of point P corresponding to the first angle and the projection on the vertical Y-axis of point Q corresponding to the second angle are equally large though opposite in sign (which can be shown by congruence).

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