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Select the trigonometric function and enter the angle in the specified field. The calculator will instantly calculate its value with the graph displayed.
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This trigonometry calculator enables you to compute all six fundamental trigonometric functions (sin, cos, tan, sec, csc, cot) for any given angle in degrees or radians.
Use this tool to quickly find the value of any trigonometric function for an angle in a right triangle.
You can also determine triangle sides using the Law of Sines calculator.
Trigonometry is the branch of mathematics that studies the relationship between angles and sides of triangles. This calculator quickly evaluates all six trigonometric ratios for any angle.
Ratio of the opposite side to the hypotenuse:
sin θ = Opposite / Hypotenuse
Ratio of the adjacent side to the hypotenuse:
cos θ = Adjacent / Hypotenuse
Ratio of the opposite side to the adjacent side:
tan θ = Opposite / Adjacent
Reciprocal of cosine (hypotenuse over adjacent):
sec θ = Hypotenuse / Adjacent
Reciprocal of sine (hypotenuse over opposite):
csc θ = Hypotenuse / Opposite
Reciprocal of tangent (adjacent over opposite):
cot θ = Adjacent / Opposite
Inverse trig functions return the angle corresponding to a given ratio:
arcsin x = sin⁻¹ x
arccos x = cos⁻¹ x
arctan x = tan⁻¹ x
arccot x = cot⁻¹ x
arcsec x = sec⁻¹ x
arccsc x = csc⁻¹ x
These functions allow you to convert ratios back into angles in degrees or radians.
| Function | Description | Relation (radians) | Relation (degrees) |
|---|---|---|---|
| sin | opposite / hypotenuse | \(\sin \theta = \cos(\frac{\pi}{2}-\theta) = \frac{1}{\csc \theta}\) | \(\sin x = \cos(90^\circ - x) = \frac{1}{\csc x}\) |
| cos | adjacent / hypotenuse | \(\cos \theta = \sin(\frac{\pi}{2}-\theta) = \frac{1}{\sec \theta}\) | \(\cos x = \sin(90^\circ - x) = \frac{1}{\sec x} |
| tan | opposite / adjacent | \(\tan \theta = \frac{\sin \theta}{\cos \theta} = \cot(\frac{\pi}{2}-\theta) = \frac{1}{\cot \theta}\) | \(\tan x = \frac{\sin x}{\cos x} = \cot(90^\circ - x) = \frac{1}{\cot x} |
| cot | adjacent / opposite | \(\cot \theta = \frac{\cos \theta}{\sin \theta} = \tan(\frac{\pi}{2}-\theta) = \frac{1}{\tan \theta} | \(\cot x = \frac{\cos x}{\sin x} = \tan(90^\circ - x) = \frac{1}{\tan x} |
| sec | hypotenuse / adjacent | \(\sec \theta = \csc(\frac{\pi}{2}-\theta) = \frac{1}{\cos \theta} | \(\sec x = \csc(90^\circ - x) = \frac{1}{\cos x} |
| csc | hypotenuse / opposite | \(\csc \theta = \sec(\frac{\pi}{2}-\theta) = \frac{1}{\sin \theta} | \(\csc x = \sec(90^\circ - x) = \frac{1}{\sin x} |
Given a right triangle with:
Trigonometric values are:
Trigonometry focuses on angles and triangle relationships, whereas calculus deals with limits, derivatives, and integrals. Calculus is typically considered more advanced.
Wikipedia: Trigonometry, Khan Academy: Radians & Degrees
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