Choose a trigonometry tool
Select an option, enter values, and view steps below.
Formula Used
These tools use standard trigonometry formulas for triangles, circles, periodic functions, coordinate conversion, and identities.
Right triangle ratios
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
Unit circle
x = cos θ, y = sin θ
tan θ = sin θ / cos θ
Triangle laws
a/sin A = b/sin B = c/sin C
c² = a² + b² − 2ab cos C
Wave features
y = A sin(Bx + C) + D
Amplitude = |A|, period = 2π / |B|
How to Use This Calculator
- Choose one trigonometry operation.
- Enter the known values.
- Select degree or radian mode carefully.
- Press Calculate with Steps.
- Review the result, table, and visual preview.
- Use CSV or print tools for saving.
Example Data Table
| Tool | Input | Main Output |
|---|---|---|
| Unit circle | θ = 225° | sin, cos, tan, quadrant |
| Right triangle | opposite 3, adjacent 4, hypotenuse 5 | six trigonometric ratios |
| Law of Cosines | a = 8, b = 11, C = 48° | third side and remaining angles |
| Wave | 2sin(3x − π/2) + 1 | amplitude, period, phase shift |
| Sector | radius 6, angle 80° | arc length, area, chord |
Trigonometry Solver Guide
Why trigonometry needs clear angle control
Trigonometry connects angles, lengths, circles, waves, and coordinate systems. A small unit mistake can change every final value. This calculator keeps degree and radian choices visible, because formulas such as arc length, sector area, and sinusoidal period depend on radians internally. Unit-circle values also become easier to understand when the same angle is shown in both formats.
Right triangles and ratios
Right triangle problems usually begin with opposite, adjacent, and hypotenuse labels. Sine, cosine, and tangent compare these sides. Once one acute angle and one side are known, all missing sides can be found. The calculator shows each ratio step, then checks area and perimeter for a complete geometric result.
Triangle solving beyond right triangles
Many triangles are not right triangles. For those cases, the Law of Sines and Law of Cosines are stronger tools. The Law of Sines works best when a matching side-angle pair is known. The Law of Cosines works well for three sides or two sides with an included angle. These methods also support area and perimeter calculations.
Functions, equations, and identities
Trigonometric functions repeat, so equation answers often come in families. A calculator should not only return one angle. It should show the period and the related angles in a full turn. Identity checks are also useful. They help verify that sine, cosine, tangent, secant, cosecant, and cotangent remain consistent.
Waves and coordinate applications
Sinusoidal equations model oscillation. The amplitude measures height from the midline. The period measures one complete cycle. The phase shift moves the graph left or right. Trigonometry also converts polar coordinates to rectangular coordinates and resolves vectors into components. These tools make the calculator useful for algebra, geometry, physics, and precalculus work.
FAQs
What does this trigonometry calculator solve?
It solves ratios, unit-circle values, right triangles, general triangles, trig equations, waves, components, coordinate conversions, sectors, and identity checks.
Can I enter radians like pi/3?
Yes. You can type values such as pi/3, -pi/2, 2*pi, fractions, or decimals in supported angle fields.
Why do arc formulas require radians?
Radians compare arc length directly with radius. That makes s = rθ and K = 1/2 r²θ valid without extra conversion factors.
Does it show reciprocal ratios?
Yes. The ratio tools show cosecant, secant, and cotangent when the required denominator is not zero.
Can it solve non-right triangles?
Yes. Use Triangle SSS, Law of Sines, or Law of Cosines tools for general triangle problems.
What is a reference angle?
A reference angle is the acute angle between the terminal side and the x-axis. It helps identify trig values by quadrant.
Why is tangent sometimes undefined?
Tangent equals sine divided by cosine. It is undefined when cosine equals zero.
Can the wave tool use cosine?
Yes. Select sine or cosine, then enter A, B, C, and D for the transformed equation.
What does phase shift mean?
Phase shift is the horizontal movement of a sinusoidal graph. For y = A sin(Bx + C) + D, it equals -C/B.
Does it solve general trig equations?
It solves basic equations of the form sin θ = k, cos θ = k, and tan θ = k over one full turn.
Can it convert polar coordinates?
Yes. It converts polar to rectangular and rectangular to polar using sine, cosine, and atan2.
Does it create a graph preview?
Yes. It draws unit-circle points, vectors, waves, sectors, or triangle sketches, depending on the selected tool.
Can I export results?
Yes. Use Download CSV for computed rows, or Print / PDF to save a printable copy.
Is this suitable for homework checks?
Yes. It is designed to show the formula, substitution, result, and visual context for each selected operation.