Trigonometry/Functions
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- See also Trigonometry/Polar for an approach that is useful for -∞<θ<∞
Fundamental trigonometry functions[edit | edit source]
There are six trigonometric functions in Trigonometry: sine, cosine, tangent, cotangent, secant, and cosecant.
Sine[edit | edit source]
- Sine θ is the length of the leg opposite θ over the length of the hypotenuse:
Cosine[edit | edit source]
- Cosine θ is the length of the leg adjacent to θ over the hypotenuse:
Tangent[edit | edit source]
- 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:
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[edit | edit source]
- Cotangent θ is the reciprocal of tangent θ:
Secant[edit | edit source]
- Secant θ is the reciprocal of cosine θ:
Cosecant[edit | edit source]
- Cosecant θ is the reciprocal of sine θ:
Other considerations[edit | edit source]
- Since the hypotenuse of a right triangle is always the longest side, and
- If we divide both sides of each of these inequalities by the positive number , we get and
or and
Table[edit | edit source]
- See Table of functions.
Quiz[edit | edit source]
Other resources[edit | edit source]
- Reading: w:Trigonometric_Functions (Wikipedia)
- Videos:
- Basic Trigonometry (Youtube)
- Basic Trigonometry II (Youtube)