Exact Values of Trigonometric Functions

Pronunciation: /ɪgˈzækt ˈvæl yuz ʌv ˌtrɪg əˈnɒm ɪ trik ˈfʌŋk ʃənz/ ?

The exact values of trigonometric functions are values of trigonometric functions of certain angles that can be expressed exactly using expressions containing real numbers and roots of real numbers.[1] These values are also called analytic values of trigonometric functions or trigonometric values of special angles. These angles are often used on tests where a calculator is not allowed, so it is useful for students to memorize these angles and the values of trigonometric functions of these angles. A mnemonic for remembering these values is at the end of this article.

Exact Values of Trigonometric Functions
Angle
Degrees
Angle
Radians
sin(θ)cos(θ)tan(θ)
0 rad010
30°pi/6 rad1/2square root(3)/2square root(3)/3
45°pi/4 radsquare root(2)/2square root(2)/21
60°pi/3 radsquare root(3)/21/2square root(3)
90°pi/2 rad01undefined
180°pi rad0-10
270°3*pi/2 rad-10undefined
Table 1

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Manipulative 1: Exact values of trigonometric functions. Created with GeoGebra.

Mnemonic What is this?

A mnemonic for remembering the values of sine for special angles is:

sin(0)=(1/2)*square root(0); sin(30)=(1/2)*square root(1); sin(45)=(1/2)*square root(2); sin(60)=(1/2)*square root(3); sin(90)=(1/2)*square root(4);
Figure 1: Mnemonic for sine of special angles

A mnemonic for the cosine values of special angles is similar:

cos(0)=(1/2)*square root(4); cos(30)=(1/2)*square root(3); cos(45)=(1/2)*square root(2); cos(60)=(1/2)*square root(1); cos(90)=(1/2)*square root(0);
Figure 1: Mnemonic for cosine of special angles

Cite this article as:


Exact Values of Trigonometric Functions. 2010-02-01. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/e/exactvaltrig.html.

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Revision History


2010-02-01: Added "References" (McAdams, David.)
2009-12-26: Combined with Analytic Values of Trigonometric Functions and added reference (McAdams, David.)
2009-01-07: Initial version (McAdams, David.)

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