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Trigonometry overview (sin ,cos, tan)
The purpose of this page is to give just enough knowledge of trigonometry to allow formulas that appear in geometry to be evaluated.
A complete separate volume is planned for this subject. This page is a temporary aid to solving geometry formulae. Only sin ,cos and tan functions are discussed here.
Angle units - degrees and radians
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 other pages in the geometry volume,
the angles are always assumed to be in radians.
If your calculator has it, switch it into 'radians' mode. It will assume the angles you enter are in radians. Otherwise you will have to convert the angle
to degrees. Some calculators have a conversion for this built in; otherwise multiply the angle by 6.284 (or two times PI) to convert it to degrees.
SIN
This is the 'sine' function. It takes a number x, which represents an angle, and gives another number, which is called the 'sine of x',
or just 'sine x'.
The angle x can be in degrees or radians (see units discussion above).
Using a calculator:
- 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)
it will be in radians. Make sure the calculator is in radians mode, or use the calculator to convert the units to degrees.
- HP calculators using RPN: Enter the angle and press sin
- Algebraic calculators: Press 'sin', then the angle, then '='.
Try this:
Calculate the sine of 1.5. (Remember - it's 1.5 radians) You should get 0.997 approx.
COS
This is the 'cosine' function. It takes a number x, which represents an angle, and gives another number, which is called the 'cosine of x',
or just 'cosine x'.
The angle x can be in degrees or radians (see units discussion above).
Using a calculator:
- 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)
it will be in radians. Make sure the calculator is in radians mode, or use the calculator to convert the units to degrees.
- HP calculators using RPN: Enter the angle and press cos
- Algebraic calculators: Press 'cos', then the angle, then '='.
Try this:
Calculate the cosine of 1.3. (Remember - it's 1.3 radians) You should get 0.267 approx.
TAN
This is the 'tangent' function. It takes a number x, which represents an angle, and gives another number, which is called the 'tangent of x',
or just 'tan x'.
The angle x can be in degrees or radians (see units discussion above).
Using a calculator:
- 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)
it will be in radians. Make sure the calculator is in radians mode, or use the calculator to convert the units to degrees.
- HP calculators using RPN: Enter the angle and press tan
- Algebraic calculators: Press 'tan', then the angle, then '='.
Try this:
Calculate the tangent of 1.5. (Remember - it's 1.5 radians) You should get 14.1 approx.
(C) 2007 Copyright John Page
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