Mastering Trigonometry: Simplifying Calculations Using Coterminal Angles

Coterminal Angles

-Angles with the same initial & terminal sides -Positive coterminal angles have a positive sign -Negative coterminal angles have a negative sign -+/- coterminal angles are found by adding or subtracting 2π (360 degrees) until the desired sign is achieved

Coterminal angles are angles that have the same initial and terminal sides but differ in the number of complete revolutions made. In other words, coterminal angles are angles that occupy the same position in the coordinate plane.

To find coterminal angles, we can add or subtract a full rotation of 360 degrees or 2π radians to the original angle. For example, if we have an angle of 45 degrees, its coterminal angles are:

405 degrees (45 degrees + 360 degrees)
-315 degrees (45 degrees – 360 degrees)

In radians, if we have an angle of π/3 radians, its coterminal angles are:

7π/3 radians (π/3 + 2π)
-5π/3 radians (π/3 – 2π)

Coterminal angles are useful in trigonometry to simplify calculations and solve problems. For example, if we need to find the sine of an angle of 495 degrees, we can find its coterminal angle by subtracting a full rotation of 360 degrees, which gives us an angle of 135 degrees. The sine of 135 degrees is the same as the sine of 495 degrees, which is -√2/2.

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