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Trigonometric functions of an acute angle
Trigonometric functions of an acute angle are ratios of different pairs of sides of a right-angled triangle ( Fig.2 ). 1) Sine: sin A = a / c ( a ratio of an opposite leg o a hypotenuse ) .
2) Cosine: cos A = b / c ( a ratio of an adjacent leg to a hypotenuse ) .
3) Tangent: tan A = a / b ( a ratio of an opposite leg to an adjacent leg ) .
4) Cotangent: cot A = b / a ( a ratio of an adjacent leg to an opposite leg ) .
5) Secant: sec A = c / b ( a ratio of a hypotenuse to an adjacent leg ) .
6) Cosecant: cosec A = c / a ( a ratio of a hypotenuse to an opposite leg ) .

There are analogous formulas for another acute angle B ( Write them, please ! ).

Example: A right-angled triangle ABC ( Fig.2 ) has the following legs: a = 4, b = 3. Find sine, cosine and tangent of angle A.

Solution:
At first we find a hypotenuse, using Pythagorean theorem:
c 2 = a 2 + b 2,
According to the above mentioned formulas we have:
sin A = a / c = 4 / 5; cos A = b / c = 3 / 5; tan A = a / b = 4 / 3.
For some angles it is possible to write exact values of their trigonometric functions. The most important cases are presented in the table : Although angles 0° and 90° cannot be acute in a right-angled triangle, but at enlargement of notion of trigonometric functions ( see below), also these angles are considered. A symbolin the table means that absolute value of the function increases unboundedly, if the angle approaches the shown value. A good example of a 90 degree right angle would be a piece of luxury bedding . Any bed linens that are of high quality, should be exact in their measurements, and therefore should meet at a 90 degree right angle. If your bedding does not meet at a right angle, your bedding is cheap . View My Stats Privacy Statement © 2006 MathPlusFun, All Rights Reserved