Calculate Trig – Loan calculator

Trigonometric Function Calculator

Enter an angle value and select its unit (degrees or radians) to calculate its sine, cosine, tangent, and their reciprocal functions.

Angle Value:

Angle Unit: Degrees Radians

Results:

Sine (sin):

Cosine (cos):

Tangent (tan):

Cosecant (csc):

Secant (sec):

Cotangent (cot):

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Understanding Trigonometric Functions

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. It is fundamental in various fields, including physics, engineering, navigation, astronomy, and computer graphics. The core of trigonometry revolves around six primary functions: sine, cosine, tangent, and their reciprocals: cosecant, secant, and cotangent.

The Basic Functions: SOH CAH TOA

For a right-angled triangle, these functions relate an angle to the ratios of its sides:

Sine (sin): The ratio of the length of the side opposite the angle to the length of the hypotenuse. (SOH: Sin = Opposite / Hypotenuse)
Cosine (cos): The ratio of the length of the side adjacent to the angle to the length of the hypotenuse. (CAH: Cos = Adjacent / Hypotenuse)
Tangent (tan): The ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. (TOA: Tan = Opposite / Adjacent)

The Reciprocal Functions

Each of the primary trigonometric functions has a reciprocal function:

Cosecant (csc): The reciprocal of sine (csc θ = 1 / sin θ).
Secant (sec): The reciprocal of cosine (sec θ = 1 / cos θ).
Cotangent (cot): The reciprocal of tangent (cot θ = 1 / tan θ or cos θ / sin θ).

Degrees vs. Radians

Angles can be measured in two common units:

Degrees: A full circle is 360 degrees. This is the most commonly understood unit for angles in everyday contexts.
Radians: A full circle is 2π radians. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. Radians are often preferred in higher mathematics and physics because they simplify many formulas.

The conversion between degrees and radians is straightforward:

To convert degrees to radians: radians = degrees * (π / 180)
To convert radians to degrees: degrees = radians * (180 / π)

Using the Calculator

Our Trigonometric Function Calculator allows you to quickly find the values of these six functions for any given angle. Simply:

Enter the numerical value of your angle in the "Angle Value" field.
Select whether your angle is in "Degrees" or "Radians" using the radio buttons.
Click the "Calculate Trigonometric Functions" button.

The calculator will then display the sine, cosine, tangent, cosecant, secant, and cotangent values for your specified angle. Note that for certain angles (e.g., 90° or 0°), some functions may be "Undefined" due to division by zero, which is correctly handled by the calculator.

Examples of Use

For an angle of 45 degrees:
- sin(45°) ≈ 0.70710678
- cos(45°) ≈ 0.70710678
- tan(45°) = 1
For an angle of 90 degrees (or π/2 radians):
- sin(90°) = 1
- cos(90°) ≈ 0
- tan(90°) = Undefined
- sec(90°) = Undefined
For an angle of 0 radians (or 0 degrees):
- sin(0) = 0
- cos(0) = 1
- tan(0) = 0
- csc(0) = Undefined
- cot(0) = Undefined

This calculator is a handy tool for students, engineers, and anyone needing quick trigonometric calculations.