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]Angle values
[edit | edit source]θ | radians | sinθ | cosθ | tanθ | cotθ | secθ | cosecθ |
---|---|---|---|---|---|---|---|
0° | 0 | 0 | 1 | 0 | undefined | 1 | undefined |
30° | π/6 | 1/2 | 2 | ||||
45° | π/4 | 1 | 1 | ||||
60° | π/3 | 1/2 | 2 | ||||
90° | π/2 | 1 | 0 | undefined | 0 | undefined | 1 |
180° | π | 0 | -1 | 0 | undefined | -1 | undefined |
270° | 3π/2 | -1 | 0 | undefined | 0 | undefined | -1 |
360° | 2π | 0 | 1 | 0 | undefined | 1 | undefined |
Quiz
[edit | edit source]Other resources
[edit | edit source]- Reading: w:Trigonometric_Functions (Wikipedia)
- Videos:
- Basic Trigonometry (Youtube)
- Basic Trigonometry II (Youtube)