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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.

Angles that differ by 180º

Ángulos que difieren 180ºIf A and B are two angles that B - A= 180º, that is,
B=180º + A, then:
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 third quadrant if you know the trigonometric functions of the angle that differs with it 180º.



If sinA = 0.766 and cosA = 0.643

Calculate the sine, cosine and tangent of the angle whose difference with A is 180.

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