standarddeviationcalculator.net

Updated

Trigonometry calculators

Calculators for the trig functions and their inverses, for solving triangles with the sine and cosine rules, and for solving and graphing trig equations. Exact values such as √3/2 appear alongside the decimals, in degrees, radians or gradians.

Which calculator do I need?

You have or wantUse
All six trig ratios of one angle, with exact valuesTrigonometric functions calculator
sin θ, or every angle whose sine is a given valueSine calculator
cos θ, arccos, or a side from the law of cosinesCosine calculator
The angle of a slope, ramp or roof pitchTangent calculator
The missing sides and angles of any triangleTriangle solver
Every solution of 2 sin x − 1 = 0 between 0° and 360°Trigonometric equation solver
Amplitude, period and phase shift of y = A sin(Bx − C) + DTrig graph calculator

Trig functions and their inverses

The value of a trig function at an angle, or the angle that gives a value.

Triangles and equations

Put the functions to work: solve triangles from three parts and equations on an interval.

Graphs

See the shape of a trig function and read its key features off the plot.

From one angle to a whole triangle

Start with the trig functions calculator when you have an angle and want its ratios. It gives all six at once, and exact forms for the standard angles. The sine, cosine and tangent pages go deeper into one function: its inverse, the right-triangle ratio, and the rule it belongs to. For a triangle, go to the triangle solver, which picks the sine rule or the cosine rule based on the parts you enter.

Worked comparison: one equation, several answers

A calculator’s sin⁻¹ key gives one angle, but sin x = 0.5 has two solutions between 0° and 360°: x = 30° and x = 180° − 30° = 150°. The general solution is x = 30° + 360°k or x = 150° + 360°k for any whole number k. The equation solver lists every solution in the interval you choose and graphs both sides, so you can see where they cross.

Triangles can have the same problem. With a = 7, b = 10 and A = 30°, the sine rule gives sin B = 10 × 0.5 ÷ 7 ≈ 0.7143. That means B ≈ 45.58° or B ≈ 134.42°. Both work, so two different triangles fit the data. This is the ambiguous SSA case, and the triangle solver draws both triangles.

Common mix-ups

  • Degrees versus radians. sin 30 is 0.5 in degree mode but about −0.988 in radian mode, because 30 radians is more than four full turns. Check the unit selector before trusting a result.
  • sin⁻¹ x is not 1/sin x. sin⁻¹ is the inverse function (arcsin). The reciprocal is cosecant, csc x.
  • Undefined tangents. tan 90° does not exist, because cos 90° = 0. The graph calculator marks these points as vertical asymptotes.

Guides to read alongside

Common questions

Should I use degrees or radians?
Use degrees for triangles, surveying and most school geometry. Use radians in calculus and physics, where formulas such as the derivative of sin x equal to cos x only hold in radians. The trig calculators let you choose the unit, and 180° = π radians.
When do I use the sine rule and when the cosine rule?
Use the sine rule when you know a side and its opposite angle plus one more part. Use the cosine rule when you know all three sides, or two sides and the angle between them. The triangle solver chooses for you and shows which rule it used.
Why does arcsin only give angles between −90° and 90°?
An inverse function must return one value, so arcsin is restricted to that range, called its principal values. Other solutions come from symmetry: if sin x = k, then 180° − x also works, and adding any multiple of 360° gives more. The sine calculator and the equation solver list them.

Written and reviewed by our editorial team. Last updated . Method and sources: how these numbers are computed.