Find Sin Cos Tan Csc Sec Cot Calculator

Easily calculate the sine, cosine, tangent, cosecant, secant, and cotangent for any angle with our Trigonometric Functions Calculator. Enter the angle in degrees or radians.

Calculate Trig Functions

Results Table

Function	Value
sin(θ)	–
cos(θ)	–
tan(θ)	–
csc(θ)	–
sec(θ)	–
cot(θ)	–

Table of trigonometric function values for the given angle.

Unit Circle Visualization

Unit circle showing the angle and its sine and cosine components.

What is a Trigonometric Functions Calculator (Sin, Cos, Tan, Csc, Sec, Cot)?

A Trigonometric Functions Calculator (Sin, Cos, Tan, Csc, Sec, Cot) is a tool that computes the values of the six fundamental trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) for a given angle. The angle can be input in either degrees or radians. These functions are fundamental in mathematics, physics, engineering, and many other fields, relating the angles of a triangle to the lengths of its sides.

This calculator is useful for students learning trigonometry, engineers solving practical problems, scientists, and anyone needing to find the values of these functions quickly and accurately. Common misconceptions involve confusing degrees and radians or misunderstanding the definitions on the unit circle, which our Trigonometric Functions Calculator (Sin, Cos, Tan, Csc, Sec, Cot) helps clarify.

Trigonometric Functions Formula and Mathematical Explanation

For an angle θ, the trigonometric functions are defined based on the ratios of the sides of a right-angled triangle or coordinates on a unit circle (a circle with radius 1 centered at the origin).

• If (x, y) is a point on the unit circle corresponding to angle θ (measured counterclockwise from the positive x-axis), then:
  • sin(θ) = y
  • cos(θ) = x
  • tan(θ) = y/x (undefined when x=0)
  • csc(θ) = 1/y = 1/sin(θ) (undefined when y=0)
  • sec(θ) = 1/x = 1/cos(θ) (undefined when x=0)
  • cot(θ) = x/y = 1/tan(θ) (undefined when y=0)

If the angle is given in degrees, it must first be converted to radians before using standard library functions, as θ (radians) = θ (degrees) × π / 180.

Variable	Meaning	Unit	Typical range
θ	The angle	Degrees or Radians	Any real number
sin(θ)	Sine of θ	Ratio (unitless)	-1 to 1
cos(θ)	Cosine of θ	Ratio (unitless)	-1 to 1
tan(θ)	Tangent of θ	Ratio (unitless)	-∞ to ∞
csc(θ)	Cosecant of θ	Ratio (unitless)	(-∞, -1] U [1, ∞)
sec(θ)	Secant of θ	Ratio (unitless)	(-∞, -1] U [1, ∞)
cot(θ)	Cotangent of θ	Ratio (unitless)	-∞ to ∞

Variables used in the Trigonometric Functions Calculator (Sin, Cos, Tan, Csc, Sec, Cot).

Practical Examples (Real-World Use Cases)

Example 1: Angle of 30 Degrees

If you enter an angle of 30 degrees into the Trigonometric Functions Calculator (Sin, Cos, Tan, Csc, Sec, Cot):

• sin(30°) = 0.5
• cos(30°) ≈ 0.8660
• tan(30°) ≈ 0.5774
• csc(30°) = 2
• sec(30°) ≈ 1.1547
• cot(30°) ≈ 1.7321

Example 2: Angle of π/4 Radians (45 Degrees)

If you enter an angle of π/4 radians (which is 45 degrees) into the Trigonometric Functions Calculator (Sin, Cos, Tan, Csc, Sec, Cot):

• sin(π/4) ≈ 0.7071
• cos(π/4) ≈ 0.7071
• tan(π/4) = 1
• csc(π/4) ≈ 1.4142
• sec(π/4) ≈ 1.4142
• cot(π/4) = 1

How to Use This Trigonometric Functions Calculator (Sin, Cos, Tan, Csc, Sec, Cot)

1. Enter the Angle: Type the numerical value of the angle into the "Angle Value" field.
2. Select the Unit: Choose whether the angle you entered is in "Degrees (°)" or "Radians (rad)" from the dropdown menu.
3. View Results: The calculator will automatically update and display the values of sin(θ), cos(θ), tan(θ), csc(θ), sec(θ), and cot(θ) in the "Results" section and the table. It will also show the angle in both radians and degrees.
4. Unit Circle: The canvas below the table visualizes the angle on the unit circle.
5. Reset: Click "Reset" to return the angle to the default value (30 degrees).
6. Copy Results: Click "Copy Results" to copy the calculated values and the input angle to your clipboard.

The results will show "Undefined" for tan and sec at 90°, 270°, etc., and for csc and cot at 0°, 180°, 360°, etc., where the denominator is zero. Our Trigonometric Functions Calculator (Sin, Cos, Tan, Csc, Sec, Cot) handles these cases.

Key Factors That Affect Trigonometric Functions Results

• Angle Value: The magnitude of the angle directly determines the values of the trigonometric functions.
• Angle Unit: Whether the angle is in degrees or radians is crucial. The conversion factor is π radians = 180 degrees. Our Trigonometric Functions Calculator (Sin, Cos, Tan, Csc, Sec, Cot) handles both.
• Quadrant: The quadrant in which the angle lies (0-90°, 90-180°, 180-270°, 270-360°) determines the sign (+ or -) of the trigonometric functions.
• Reference Angle: The acute angle that the terminal side of the angle makes with the x-axis. It helps find the values in different quadrants.
• Periodicity: Trigonometric functions are periodic (e.g., sin(θ) = sin(θ + 360°) or sin(θ + 2π)).
• Undefined Points: Tangent and secant are undefined at odd multiples of 90° (π/2 radians), while cosecant and cotangent are undefined at multiples of 180° (π radians) because they involve division by zero at these angles. This is clearly indicated by the Trigonometric Functions Calculator (Sin, Cos, Tan, Csc, Sec, Cot).

Frequently Asked Questions (FAQ)

What are radians?

Radians are a unit of angle measure based on the radius of a circle. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius. 2π radians = 360 degrees.

What is the unit circle?

The unit circle is a circle with a radius of 1 centered at the origin of the Cartesian coordinate system. It's used to define trigonometric functions for all real-numbered angles.

When is tan(θ) undefined?

Tangent is undefined when cos(θ) = 0, which occurs at θ = 90° + n*180° (or π/2 + n*π radians), where n is an integer.

When are csc(θ) and cot(θ) undefined?

Cosecant and cotangent are undefined when sin(θ) = 0, which occurs at θ = n*180° (or n*π radians), where n is an integer.

Can I enter negative angles in the Trigonometric Functions Calculator (Sin, Cos, Tan, Csc, Sec, Cot)?

Yes, the calculator accepts negative angle values.

How precise are the results from the Trigonometric Functions Calculator (Sin, Cos, Tan, Csc, Sec, Cot)?

The results are calculated using standard JavaScript Math functions, providing high precision, typically to about 15-17 decimal places, though we display fewer for readability.

What's the difference between sine and cosecant?

Cosecant is the reciprocal of sine: csc(θ) = 1/sin(θ).

What's the relationship between the functions?

sin²(θ) + cos²(θ) = 1, tan(θ) = sin(θ)/cos(θ), csc(θ) = 1/sin(θ), sec(θ) = 1/cos(θ), cot(θ) = 1/tan(θ).

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