Trigonometry/Functions


 * See also Trigonometry/Polar for an approach that is useful for -&infin;<&theta;<&infin;

Fundamental trigonometry functions
There are six trigonometric functions in Trigonometry: sine, cosine, tangent, cotangent, secant, and cosecant.


 * [[Image:TrigTriangle.svg|200px]]

Sine

 * Sine θ is the length of the leg opposite θ over the length of the hypotenuse: $$\sin\theta=\frac{opp}{hyp}$$

Cosine

 * Cosine θ is the length of the leg adjacent to θ over the hypotenuse: $$\cos\theta=\frac{adj}{hyp}$$

Tangent

 * Tangent of θ is the length of the leg on the opposite side of the triangle from the angle θ over the length of the leg of the triangle adjacent to the angle θ: $$\tan\theta=\frac{opp}{adj}$$

These three can be memorized by use of the name of the princess "Soh Cah Toa," meaning:
 * "sine-opposite-hypotenuse
 * cosine-adjacent-hypotenuse
 * tangent-opposite-adjacent".

The remaining ratios are reciprocals of the previous ratios:

Cotangent

 * Cotangent θ is the reciprocal of tangent θ: $$\cot\theta=\frac{adj}{opp}$$

Secant

 * Secant θ is the reciprocal of cosine θ: $$\sec\theta=\frac{hyp}{adj}$$

Cosecant

 * Cosecant θ is the reciprocal of sine θ: $$\csc\theta=\frac{hyp}{opp}$$

Other considerations

 * Since the hypotenuse of a right triangle is always the longest side, $$opp < hyp\,$$ and $$adj < hyp\,$$
 * If we divide both sides of each of these inequalities by the positive number $$hyp\,$$, we get $$\frac{opp}{hyp} < \frac{hyp}{hyp}\,$$ and $$\frac{adj}{hyp} < \frac{hyp}{hyp}\,$$ or $$\sin \theta \leq 1\,$$ and $$\cos \theta \leq 1\,$$

Quiz

 * Trigonometry/Functions/Quiz

Other resources

 * Reading: Trigonometric_Functions (Wikipedia)
 * Videos:
 * Basic Trigonometry (Youtube)
 * Basic Trigonometry II (Youtube)


 * Trigonometry/Functions/Flash cards