Find Sine Cosine Tangent Calculator

Instantly find the sine, cosine, and tangent of any angle with our easy-to-use Sine Cosine Tangent Calculator.

Trigonometric Functions Calculator

Common Angles and Their Trig Values

Sine, Cosine, and Tangent values for common angles.

Angle (Degrees)	Angle (Radians)	Sine (sin θ)	Cosine (cos θ)	Tangent (tan θ)
0°	0	0	1	0
30°	π/6 (≈0.5236)	0.5	√3/2 (≈0.8660)	1/√3 (≈0.5774)
45°	π/4 (≈0.7854)	1/√2 (≈0.7071)	1/√2 (≈0.7071)	1
60°	π/3 (≈1.0472)	√3/2 (≈0.8660)	0.5	√3 (≈1.7321)
90°	π/2 (≈1.5708)	1	0	Undefined
180°	π (≈3.1416)	0	-1	0
270°	3π/2 (≈4.7124)	-1	0	Undefined
360°	2π (≈6.2832)	0	1	0

What is a Sine Cosine Tangent Calculator?

A Sine Cosine Tangent Calculator is a tool used to determine the values of the three primary trigonometric functions: sine (sin), cosine (cos), and tangent (tan) for a given angle. The angle can typically be input in either degrees or radians. These functions are fundamental in trigonometry, a branch of mathematics that studies relationships involving lengths and angles of triangles, particularly right-angled triangles.

These functions relate the angles of a right triangle to the ratios of the lengths of its sides. The Sine Cosine Tangent Calculator simplifies the process of finding these ratios, which are widely used in various fields like physics, engineering, navigation, computer graphics, and more.

Who Should Use It?

• Students: Learning trigonometry and needing to verify their calculations or understand the relationship between angles and side ratios.
• Engineers: For calculations involving forces, waves, oscillations, and structural analysis.
• Physicists: In mechanics, optics, and wave theory.
• Navigators and Surveyors: To determine positions and distances.
• Game Developers and Graphic Designers: For rotations, transformations, and creating realistic movements.

Common Misconceptions

• Only for Right Triangles: While defined using right triangles (SOH CAH TOA), sine, cosine, and tangent are applicable to all angles (0 to 360 degrees and beyond, or 0 to 2π radians and beyond) using the unit circle definition, extending their use beyond just right triangles.
• Units Don’t Matter: The input angle unit (degrees or radians) drastically changes the result. A Sine Cosine Tangent Calculator requires you to specify the unit.
• Tangent is Always Defined: The tangent function is undefined at 90°, 270°, and other angles where the cosine is zero.

Sine Cosine Tangent Calculator Formula and Mathematical Explanation

The trigonometric functions sine, cosine, and tangent are most easily defined for an acute angle (θ) within a right-angled triangle:

• Sine (sin θ) = Opposite / Hypotenuse
• Cosine (cos θ) = Adjacent / Hypotenuse
• Tangent (tan θ) = Opposite / Adjacent

Where:

• Opposite: The length of the side opposite to the angle θ.
• Adjacent: The length of the side adjacent (next) to the angle θ, but not the hypotenuse.
• Hypotenuse: The length of the longest side, opposite the right angle.

This is often remembered by the mnemonic SOH CAH TOA.

For angles beyond 90° (or outside a right triangle context), these functions are defined using the unit circle (a circle with radius 1 centered at the origin of a Cartesian coordinate system). If a point (x, y) is on the unit circle at an angle θ from the positive x-axis:

• sin θ = y
• cos θ = x
• tan θ = y/x (undefined when x=0)

Our Sine Cosine Tangent Calculator uses these definitions. If you input an angle in degrees, it first converts it to radians because most programming language math functions (like JavaScript’s `Math.sin()`, `Math.cos()`, `Math.tan()`) expect the angle in radians:

Angle in Radians = Angle in Degrees × (π / 180)

Variables Table

Variable	Meaning	Unit	Typical Range
θ (Angle)	The input angle for which trig functions are calculated	Degrees or Radians	0-360° or 0-2π rad (but can be any real number)
sin θ	Sine of the angle θ	Dimensionless ratio	-1 to 1
cos θ	Cosine of the angle θ	Dimensionless ratio	-1 to 1
tan θ	Tangent of the angle θ	Dimensionless ratio	-∞ to ∞ (undefined at 90°, 270°, etc.)

Variables used in the Sine Cosine Tangent Calculator.

Practical Examples (Real-World Use Cases)

Example 1: Finding the Height of a Tree

Imagine you are standing 20 meters away from the base of a tree. You measure the angle of elevation from your eye level to the top of the tree to be 40 degrees. You want to find the height of the tree above your eye level.

• Angle (θ) = 40 degrees
• Adjacent side (distance from tree) = 20 meters
• Opposite side (height above eye level) = h (unknown)

We use tan θ = Opposite / Adjacent => tan 40° = h / 20.

Using a Sine Cosine Tangent Calculator or trigonometric tables, tan 40° ≈ 0.8391.

So, h = 20 * 0.8391 ≈ 16.78 meters. If your eye level is 1.5 meters, the total tree height is 16.78 + 1.5 = 18.28 meters.

Example 2: Analyzing an AC Circuit

In electronics, the voltage in an AC circuit can be represented by V(t) = V₀ sin(ωt + φ), where V₀ is the peak voltage, ω is the angular frequency, t is time, and φ is the phase angle. If V₀=120V, ω=100π rad/s, and we want to find the voltage at t=0.005s with φ=0, we need sin(100π * 0.005) = sin(0.5π radians) or sin(90 degrees).

Using our Sine Cosine Tangent Calculator for 90 degrees (or 0.5π radians): sin(90°) = 1.

So, V(0.005) = 120 * 1 = 120V (the peak voltage).

How to Use This Sine Cosine Tangent Calculator

1. Enter the Angle: Type the angle value into the “Enter Angle” input field.
2. Select the Unit: Choose whether the angle you entered is in “Degrees” or “Radians” using the radio buttons.
3. Calculate: Click the “Calculate” button (or the results will update automatically as you type/select).
4. View Results: The calculator will display the sine, cosine, and tangent of the angle, along with the angle converted to radians (if input was in degrees).
5. Reset: Click “Reset” to clear the input and results and return to default values.
6. Copy Results: Click “Copy Results” to copy the angle, unit, sine, cosine, and tangent values to your clipboard.

How to Read Results

The results section shows:

• The angle you entered and its unit.
• The calculated Sine value.
• The calculated Cosine value.
• The calculated Tangent value (will show “Undefined” if the cosine is zero).
• The angle converted to radians if you input degrees.

The Sine Cosine Tangent Calculator provides direct numerical values for these functions.

Key Factors That Affect Sine Cosine Tangent Calculator Results

1. Angle Value: The primary input, directly determines the sin, cos, and tan values.
2. Angle Unit (Degrees or Radians): Critically important. sin(30 degrees) is 0.5, but sin(30 radians) is very different. Ensure you select the correct unit. Our Sine Cosine Tangent Calculator handles both.
3. Quadrant of the Angle: The sign (+ or -) of sine, cosine, and tangent depends on which quadrant (0-90°, 90-180°, 180-270°, 270-360°) the angle lies in.
4. Calculator Precision: The number of decimal places the calculator uses can affect the precision of the result, although our Sine Cosine Tangent Calculator uses standard JavaScript `Math` functions for high precision.
5. Reference Angle: For angles outside 0-90°, the values are related to those of a reference angle within the first quadrant.
6. Special Angles: Angles like 0°, 30°, 45°, 60°, 90°, and their multiples have exact, often simple, values for sin, cos, and tan (e.g., sin 30° = 0.5, cos 60° = 0.5).

Frequently Asked Questions (FAQ)

Q1: What are sine, cosine, and tangent?

A1: They are the three main trigonometric functions that relate an angle of a right-angled triangle to the ratios of the lengths of its sides. They are also defined for all angles using the unit circle.

Q2: What is the range of sine and cosine values?

A2: The values of sine and cosine range from -1 to +1, inclusive.

Q3: What is the range of tangent values?

A3: The tangent function can take any real value from -∞ to +∞. It is undefined at 90°, 270°, etc.

Q4: Why is tangent undefined at 90 degrees?

A4: Because tan θ = sin θ / cos θ, and at 90 degrees, cos 90° = 0. Division by zero is undefined. In the right triangle context, the adjacent side would be zero.

Q5: What’s the difference between degrees and radians?

A5: They are two different units for measuring angles. A full circle is 360 degrees or 2π radians. 180 degrees = π radians. Our Sine Cosine Tangent Calculator allows input in both.

Q6: How do I convert degrees to radians?

A6: Multiply the angle in degrees by π/180. You can also use our radian to degree converter.

Q7: How do I convert radians to degrees?

A7: Multiply the angle in radians by 180/π.

Q8: Can I use this Sine Cosine Tangent Calculator for negative angles?

A8: Yes, enter a negative value for the angle. sin(-θ) = -sin(θ), cos(-θ) = cos(θ), tan(-θ) = -tan(θ).