Calculator Input
Generated Angle Table
| Angle | Unit | Degrees | Radians | Cosine | Tangent | Quadrant |
|---|---|---|---|---|---|---|
| 0 | Degrees | 0 | 0 | 1 | 0 | Positive x-axis |
| 15 | Degrees | 15 | 0.261799 | 0.965926 | 0.267949 | Quadrant I |
| 30 | Degrees | 30 | 0.523599 | 0.866025 | 0.57735 | Quadrant I |
| 45 | Degrees | 45 | 0.785398 | 0.707107 | 1 | Quadrant I |
| 60 | Degrees | 60 | 1.047198 | 0.5 | 1.732051 | Quadrant I |
| 75 | Degrees | 75 | 1.308997 | 0.258819 | 3.732051 | Quadrant I |
| 90 | Degrees | 90 | 1.570796 | 0 | Undefined | Positive y-axis |
Example Data Table
| Angle | Cosine | Tangent | Common note |
|---|---|---|---|
| 0° | 1 | 0 | Starts on the positive x-axis. |
| 30° | 0.866025 | 0.577350 | Common special angle. |
| 45° | 0.707107 | 1 | Opposite and adjacent sides match. |
| 60° | 0.5 | 1.732051 | Tangent is greater than one. |
| 90° | 0 | Undefined | Cosine is zero. |
| 180° | -1 | 0 | Point lies on the negative x-axis. |
Formula Used
The calculator uses standard trigonometric ratios and unit conversion rules.
- cos(θ) = adjacent side / hypotenuse
- tan(θ) = opposite side / adjacent side
- tan(θ) = sin(θ) / cos(θ)
- degrees = radians × 180 / π
- radians = degrees × π / 180
- gradians = degrees × 10 / 9
- inverse tangent angle = arctan(value)
- inverse cosine angle = arccos(value)
Tangent is undefined when cosine is zero. This happens at 90° and 270°, plus full rotations.
How To Use This Calculator
- Select the calculation mode.
- Enter an angle or inverse ratio value.
- Choose degrees, radians, or gradians.
- Set decimal places for rounded output.
- Enter table start, end, and step values.
- Press Calculate to view results below the header.
- Use CSV or PDF buttons to save the report.
Tan And Cos Calculator Guide
Overview
Tan and cosine values support many daily math tasks. They connect an angle with a ratio. This calculator makes that work easier. It accepts common angle units. It also gives clear supporting values. You can review radians, degrees, quadrant data, reference angle, and related ratios.
Why These Ratios Matter
Cosine compares the adjacent side with the hypotenuse. Tangent compares the opposite side with the adjacent side. These ratios help describe slope, rotation, waves, navigation, and circular motion. They also support design checks and classroom practice. A small angle change can cause a large tangent change near ninety degrees. For that reason, the page warns when tangent is undefined.
Useful Advanced Options
The calculator supports degrees, radians, and gradians. It can calculate from an angle. It can also reverse a tangent or cosine value. Decimal control helps match homework, reports, or engineering notes. The table builder creates repeated angle checks. Use it to compare a range of values without entering every angle again. Export tools help save the result for later review.
Reading The Results
The main result shows cosine and tangent first. Extra rows explain the normalized angle, quadrant, reference angle, period notes, and related values. Secant and cotangent are shown when possible. They are marked undefined when division by zero would occur. The equivalent angle section helps you see how periodic functions repeat.
Good Practice Tips
Always choose the correct input unit. Degree and radian mistakes are common. Check whether the problem expects exact values or decimal values. Use more decimals for technical work. Use fewer decimals for quick estimates. When tangent becomes very large, inspect the cosine value. A cosine near zero means the angle is near a vertical line.
Practical Uses
Students can verify trigonometry exercises. Teachers can prepare examples. Builders can estimate slopes. Designers can compare rotation values. Analysts can create quick reference tables. The calculator is not a replacement for proofs. It is a practical checking tool. Use it with diagrams, formulas, and careful units. This gives stronger results and fewer mistakes.
Common Mistakes
Do not round too early during multi-step work. Keep original angle values for exports. Check signs by quadrant. Remember that cosine repeats every full turn. Tangent repeats every half turn always.
FAQs
What does tangent measure?
Tangent measures the ratio of the opposite side to the adjacent side in a right triangle. It also describes slope and direction from an angle.
What does cosine measure?
Cosine measures the ratio of the adjacent side to the hypotenuse. On the unit circle, it is the x-coordinate of the angle point.
Why is tangent sometimes undefined?
Tangent equals sine divided by cosine. When cosine is zero, division is not possible. That makes tangent undefined at those angles.
Which angle unit should I choose?
Use the unit given in your problem. Degrees are common in school examples. Radians are common in calculus, physics, and programming work.
Can this calculator use negative angles?
Yes. Negative angles are accepted. The calculator also shows normalized degrees, so you can compare them with standard circle positions.
What does inverse tangent mode do?
Inverse tangent mode takes a tangent value and returns the principal angle. The result is then used to calculate cosine and tangent again.
What does inverse cosine mode do?
Inverse cosine mode takes a cosine value from -1 to 1. It returns the principal angle from zero to pi radians.
What is a reference angle?
A reference angle is the acute angle formed with the x-axis. It helps compare trigonometric values across different quadrants.