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Maths Exercices
Trigonometric functions at related angles

Using the geometric symmetry of the unit circle, some trigonometric functions can be established. You can calculate the trigonometric functions of an angle in the second, third or fourth quadrant using its ratio with the first quadrant.

Supplementary angles.
Two angles are supplementary if they add up to 180 degrees.

Ángulo suplementarioIf A and B are two angles where A+B=180º , that is, B=180º - A, we have:
sinA = sin B, so that, sin A = sin(180º-A)
cosA = -cos B , so that, cosA = -cos(180º-A)
Similarly tanA = -tanB

Using these formulas, you can calculate the trigonometric functions of an angle in the second quadrant if you know the trigonometric functions of its supplementary angle.


If sinA = 0.866 and cosA = 0.5

Calculate the sine, cosine and tangent of the supplementary angle of A.

Solution: Sine = Cosine = Tangent =
(round the solution to thousandths)