Sine, Cosine, and Tangent Ratios (Leaving Cert Mathematics): Flashcards

Special relationships between sides and angles of right-angled triangles

Sine, cosine, and tangent

Longest side opposite the right angle

Side opposite to the angle being considered

Side next to the angle (not the hypotenuse)

$\sin A = \frac{\text{opposite}}{\text{hypotenuse}}$

$\cos A = \frac{\text{adjacent}}{\text{hypotenuse}}$

$\tan A = \frac{\text{opposite}}{\text{adjacent}}$

SOH: Sine=Opp/Hyp, CAH: Cos=Adj/Hyp, TOA: Tan=Opp/Adj

$\sin^2 A + \cos^2 A = 1$ (always true for any angle)

Always, for any angle $A$

3-4-5 triangle (Pythagorean triple)

5-12-13 triangle (Pythagorean triple)

Always the longest side