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Trigonometric Function Calculator

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(calculates one of the six trigonometric functions given either a degree or radian value)

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Trigonometric Functions Tutorial

The six trigonometric functions are sin, cos, tan, csc, sec, and cot. These trig functions allow you to find missing sides of triangles. Trig functions are ratios in a right triangle relative to an angle. Sin of an angle is the ratio of the side length opposite to the angle to the hypotenuse length. Cos of an angle is the ratio of the side length adjacent to the angle to the hypotenuse length. Tan is the ratio of the opposite side length to the adjacent side length. Csc is the reciprocal of sin or the ratio of the hypotenuse to the opposite side instead of the opposite side to the hypotenuse. Sec is the reciprocal of cos or the ratio of the hypotenuse to the adjacent side. Cot is the reciprocal of tan or the ratio of the adjacent side to the opposite side. The way these trig functions are used to find missing sides in a right triangle is shown in the example below. If a right triangle has an angle or measure 27 degrees and a hypotenuse of length 88. The sin function will allow you to find the opposite side length of the triangle. The calculation process for this is shown below.

\sin (\text{angleA})=\frac{\text{opposite}}{\text{hypotenuse}}

\sin (\text{angleA})=\frac{(\text{sideA})}{(\text{sideC})}

\sin ((27))=\frac{\text{sideA}}{(88)}

\text{sideA}=\sin (27)\cdot 88

\text{sideA}=39.9511639770801177



Once the opposite side length is known, the cos function can be used to find the adjacent side length of the triangle. The calculation process for this is shown below:

\cos (\text{angleA})=\frac{(\text{sideB})}{(\text{sideC})}

\cos ((27))=\frac{\text{sideB}}{(88)}

\text{sideB}=\cos (27)\cdot 88

\text{sideB}=88\cos (27)

\text{sideB}=78.4085741285763719

Given only two sides of a right triangle it is also possible to find any angles in a right triangle. If given sides only, inverse trigonometric functions must be used to find the angle measures. The inverse trig functions are arcsin, arccos, arctan, arccsc, arcsec, and arccot. The example below demonstrates the process involved in calculating angle measures given two side lengths of a right triangle. If the hypotenuse of a triangle is of length 34 and the side length adjacent to an unknown angle has length 14, the calculation process shown below can be used.
\cos (\text{angleA})=\frac{\text{adjacent}}{\text{hypotenuse}}

\cos (\text{angleA})=\frac{\text{sideB}}{\text{sideC}}

\cos (\text{angleA})=\frac{(14)}{(34)}

\text{angleA}=\cos ^{-1}(\frac{14}{34})

\text{angleA}=65.684260828823524^\circ