Sin Cosine Tangent Calculator - Sine, Cosine, and Tangent Together

A sin cosine tangent calculator is a tool that turns any real angle into the three foundational trigonometric ratios at once: the sine, the cosine, and the tangent. Enter a single angle, pick whether you typed it in degrees, radians, or multiples of pi, and the result panel returns the dimensionless sine, cosine, and tangent side by side, along with the unit-circle quadrant and a Pythagorean identity check. Computing all three ratios together is faster than three separate lookups.

• • Right-triangle side ratios: Recover opposite, adjacent, and hypotenuse ratios from a single angle using SOH-CAH-TOA.
• • Unit-circle coordinates: Read the (cosine, sine) coordinates of a point on the unit circle.
• • Wave and signal amplitude: Evaluate the sine, cosine, and tangent components of a periodic signal at a specific phase angle.
• • Trigonometry homework and reference values: Confirm reference values like sin(45) = sqrt(2)/2, cos(45) = sqrt(2)/2, and tan(45) = 1.

All three ratios are periodic, so the same output repeats every 2*pi radians or 360 degrees. The calculator reduces the input to the principal branch in [0, 2*pi) before reporting the three ratios, so 390 degrees and 30 degrees return identical results.

Sine and cosine are bounded between -1 and 1, but tangent is not. Tangent equals sine divided by cosine and is undefined whenever cosine is exactly zero, which happens at odd multiples of pi/2 radians.

When the same angle also defines a real right triangle, Right Triangle Calculator carries the three ratios through to the missing side lengths and the remaining angles in one workflow.

The calculator reads the angle and the unit, converts the angle to radians, reduces it to the principal branch, then evaluates sine, cosine, and tangent of the reduced angle. The tangent is computed as sine divided by cosine so the result is internally consistent with the other two ratios.

• angleValue: The numeric angle you enter. Combined with angleUnit, it is the input to all three functions.
• angleUnit: The unit of the input angle: degrees, radians, or multiples of pi.
• theta (radians): The input angle expressed in radians, reduced modulo 2*pi before display.
• sine: The dimensionless output of sin(theta). Always lies in [-1, 1].
• cosine: The dimensionless output of cos(theta). Always lies in [-1, 1].
• tangent: The ratio of sine to cosine. Undefined whenever cosine is zero.

Because tangent is computed as sine divided by cosine inside the same function, the three rows in the result panel always satisfy tan = sin / cos whenever tangent is defined.

The unit-circle quadrant is computed from the sign of the reduced sine and cosine. Quadrant I has both positive, Quadrant II has sine positive and cosine negative, Quadrant III has both negative, and Quadrant IV has sine negative and cosine positive.

According to Wikipedia: Trigonometric functions, the sine of an angle equals the opposite-side length of a right triangle divided by the hypotenuse, cosine equals adjacent divided by hypotenuse, and tangent equals opposite divided by adjacent, with the same values also equal to the (y, x) coordinates of the corresponding point on the unit circle.

If the downstream problem only needs the sine, Sin Calculator focuses on the y-coordinate read-out and the unit-circle quadrant without the cosine and tangent rows in the way.

Four ideas make the three rows of the result panel read correctly.

The right-triangle interpretation and the unit-circle interpretation are the same trig function viewed from two angles. Right-triangle work emphasizes the side ratios and the 90-degree corner, while unit-circle work emphasizes the periodic, signed nature of the ratios.

Tangent is the slope of the radius line on the unit circle, which is a quick way to predict sign changes. In Quadrant I the slope is positive, in Quadrant II the slope is negative, in Quadrant III the slope is positive, and in Quadrant IV the slope is negative.

When a problem hands you a tangent value and asks for the angle that produced it, Arctan Calculator runs the inverse workflow and returns the principal angle in (-pi/2, pi/2) radians.

Four short steps are enough to get a trustworthy sine, cosine, and tangent value for any angle.

1. 1 Pick the angle unit: Select degrees, radians, or multiples of pi in the angle unit dropdown.
2. 2 Enter the angle: Type the numeric angle in the angle value field. For 'Multiples of pi', enter 0.5 for pi/2, 1 for pi, and 1.5 for 3*pi/2.
3. 3 Read the three ratios: The result panel shows the dimensionless sine, cosine, and tangent of the reduced angle. Sine and cosine always lie in [-1, 1], and tangent can be any real number or 'undefined'.
4. 4 Check the quadrant and the identity: Below the three ratios, the panel reports the unit-circle quadrant of the reduced angle and the value of sin^2 + cos^2, which should be 1 within floating-point precision.

Practical example: set the unit to degrees, enter 45, and the panel shows sine = 0.707107, cosine = 0.707107, tangent = 1, Quadrant I, and a Pythagorean identity check of 1.000000.

If the input angle arrives in degrees, minutes, and seconds or in gradians, Angle Converter reformats it to a plain decimal angle before the three ratios run.

A combined trig tool removes the need to run three separate lookups and surfaces the unit-circle geometry and the Pythagorean identity at the same time.

• • All three ratios in one place: Sine, cosine, and tangent appear in a single result panel so the three values are always read together and consistently satisfy tan = sin / cos when defined.
• • Three input units on the same form: The unit toggle accepts degrees, radians, and multiples of pi, which removes the separate degrees-to-radians step.
• • Built-in undefined handling: When cosine is zero and tangent is undefined, the panel shows 'undefined' instead of returning a misleadingly large number or a NaN.
• • Pythagorean identity sanity check: The sin^2 + cos^2 row should be 1 for any real angle, so the panel doubles as a quick check on the two ratios above it.
• • Pairs with the inverse trig tools: When a problem hands you one of the three ratios and asks for the angle that produced it, the arcsin, arccos, and arctan calculators run the inverse workflow without changing units.

The result panel keeps sine, cosine, and tangent tied together, so a sign error is straightforward to spot: if sine reads positive but cosine reads negative, the reduced angle is in Quadrant II, and tangent must be negative.

The Pythagorean identity row is the cleanest way to confirm that the calculator is reading the input angle the way you expect. Any deviation from 1 is a strong signal that the unit toggle does not match the source of the angle.

When the surrounding problem needs a full triangle workflow, Triangle Calculator carries the side lengths, the missing angle, and the area through one calculation rather than rebuilding the geometry by hand.

Four variables determine the three ratios on the panel, and two limitations tell you when the result is on the edge of validity.

• • The tool returns the principal real angle. It does not evaluate the complex-valued trigonometric functions.
• • Floating-point arithmetic means the Pythagorean identity check is only equal to 1 to roughly 15 significant digits, and the tangent 'undefined' boundary is only detected when cosine is within about 1e-12 of zero.

The principal-branch reduction is what makes 390 degrees return the same three ratios as 30 degrees.

When cosine is exactly zero on paper but a tiny nonzero number in floating-point, the calculator rounds cosine to zero and reports tangent as 'undefined' rather than producing a very large value.

According to Wolfram MathWorld: Sine, the sine and cosine functions satisfy the Pythagorean identity sin^2(theta) + cos^2(theta) = 1 for any real angle theta, which is why every point on the unit circle lies exactly one unit from the origin.

According to Wolfram MathWorld: Tangent, the tangent of an angle equals sin(theta) divided by cos(theta) and is undefined whenever cos(theta) equals zero, which happens at odd multiples of pi/2 radians.