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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.

Opposite angles.
Two angles are opposite angles if they add up to 0º or a multiple of 360º.

If A and B are two angles that B - A= k·360º where k is an integer, then:
sinA = -sin B, so that, sin A = -sin(-A)
cosA = cos B , so that, cosA = cos(-A)
Similarly tanA = - tanB

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



If sinA = 0.966 and cosA = 0.259

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

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