Exact Value of Trig Functions
Compute the exact values of sine, cosine, and tangent for common angles. Free online trigonometry calculator finds sin theta, cos theta, and tan theta for degrees and radians with all six trig functions.
About This Calculator
The Exact Value of Trig Functions Calculator computes all six trigonometric functions (sin, cos, tan, csc, sec, cot) for any angle in degrees or radians. For special angles (0 deg, 30 deg, 45 deg, 60 deg, 90 deg, and their radian equivalents), the values have exact expressions using square roots.
Trigonometric functions are fundamental to mathematics, physics, engineering, music theory, and computer graphics. They describe periodic phenomena including sound waves, light waves, planetary motion, and alternating current electricity.
Frequently Asked Questions
What are the six trigonometric functions?
The six basic trigonometric functions are sine (sin), cosine (cos), tangent (tan), cosecant (csc = 1/sin), secant (sec = 1/cos), and cotangent (cot = 1/tan). They describe relationships between angles and side lengths in right triangles.
What are the special angles in trigonometry?
The special angles are 0 deg, 30 deg, 45 deg, 60 deg, and 90 deg (in degrees) or 0, pi/6, pi/4, pi/3, pi/2 (in radians). These angles have exact trigonometric values expressed with square roots, like sin(30 deg) = 1/2 and sin(60 deg) = sqrt3/2.
How do you convert degrees to radians?
To convert degrees to radians, multiply by pi/180. To convert radians to degrees, multiply by 180/pi. For example, 180 deg = pi radians, 90 deg = pi/2 radians, and 45 deg = pi/4 radians.
Is this calculator free?
Yes, all calculators on Calculy are completely free to use.