The purpose of this page is to give just enough knowledge of trigonometry to allow formulas that appear in geometry to be evaluated.
Only sin, cos and tan functions and their inverses are discussed here.

For a full discussion see The six trigonometric functions.

All three functions (sin,cos, tan) take an angle and give another number based on that angle. The angle can be measured in degrees or radians. There are 360 degrees in a full circle, and approximately 6.284 radians in a full circle (actually two times Pi).

In the formulas given on geometry pages the angles are usually in degrees. For geometry problems in degrees, make sure your calculator is in degrees mode. This is the most common reason for strange answers.

- First determine what units are being used for x. If you are solving a formula given on other pages (example sides of a regular polygon) check whether it expects the angle to be in degrees or radians and set the calculator accordingly.
- HP calculators using RPN: Enter the angle and press sin
- Algebraic calculators: Press 'sin', then the angle, then '='.

Calculate the sine of 1.5 radians. You should get 0.997 approx.

- First determine what units are being used for x. If you are solving a formula given on other pages (example sides of a regular polygon) check whether it expects the angle to be in degrees or radians and set the calculator accordingly.
- HP calculators using RPN: Enter the angle and press cos
- Algebraic calculators: Press 'cos', then the angle, then '='.

Calculate the cosine of 45 degrees. You should get 0.707 approx.

- First determine what units are being used for x. If you are solving a formula given on other pages (example sides of a regular polygon) check whether it expects the angle to be in degrees or radians and set the calculator accordingly.
- HP calculators using RPN: Enter the angle and press tan
- Algebraic calculators: Press 'tan', then the angle, then '='.

Calculate the tangent of 80°. You should get 5.67 approx.

The three functions above each have corresponding inverse functions. They have the same names but with 'arc' in front. Just as sin x gives the sine of x, so arcsin x gives you the angle whose sin is x; the function goes the other way.

For more on this see Inverse trigonometric functions.

So for example the sin of 50 degrees is 0.766.

The arcsin of 0.766 is 50 degrees.

The three inverse functions are

arcsin x | gives the angle whose sin is x |

arcscos x | gives the angle whose cos is x |

arctan x | gives the angle whose tan is x |

- Angle definition, properties of angles
- Standard position on an angle
- Initial side of an angle
- Terminal side of an angle
- Quadrantal angles
- Coterminal angles
- Reference angle

- Introduction to the six trig functions
- Functions of large and negative angles
- Inverse trig functions
- SOH CAH TOA memory aid
- Sine function (sin) in right triangles
- Inverse sine function (arcsin)
- Graphing the sine function
- Sine waves
- Cosine function (cos) in right triangles
- Inverse cosine function (arccos)
- Graphing the cosine function
- Tangent function (tan) in right triangles
- Inverse tangent function (arctan)
- Graphing the tangent function
- Cotangent function cot (in right triangles)
- Secant function sec (in right triangles)
- Cosecant function csc (in right triangles)

- The general approach
- Finding slant distance along a slope or ramp
- Finding the angle of a slope or ramp

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