The Trigonometric Calculator helps you solve trigonometric functions including sine, cosine, tangent, and their inverse functions. It provides step-by-step explanations for each calculation, making it perfect for students learning trigonometry, engineers working with angles, and anyone needing precise trigonometric calculations. The calculator handles both degrees and radians, automatically converting between units as needed.

Required Inputs & Typical Use Cases

• Operation

  Select the trigonometric function: sin, cos, tan, csc, sec, cot, arcsin, arccos, or arctan.

• Angle Value

  Enter the angle value you want to calculate. For inverse functions, enter the ratio value (e.g., 0.5 for arcsin).

• Unit

  Choose between degrees or radians for the input angle. For inverse functions, this indicates the desired output unit.

Common scenarios: (1) Calculate sin(30°) for basic trigonometry; (2) Find cos(π/4) in radians; (3) Determine tan(45°) for right triangle problems; (4) Solve arcsin(0.5) for inverse functions; (5) Convert between degrees and radians while calculating trigonometric values.

The Formula

sin(θ) = opposite/hypotenuse
cos(θ) = adjacent/hypotenuse
tan(θ) = opposite/adjacent
csc(θ) = 1/sin(θ)
sec(θ) = 1/cos(θ)
cot(θ) = 1/tan(θ)
arcsin(x) = θ where sin(θ) = x
arccos(x) = θ where cos(θ) = x
arctan(x) = θ where tan(θ) = x

• θ

  Angle in degrees or radians

• x

  Input value for inverse functions

• Result

  Calculated trigonometric value

Worked Example

1. Step 1: Select function

   Choose the trigonometric function you need (sin, cos, tan, etc.).

2. Step 2: Enter angle

   Input the angle value you want to calculate. For inverse functions, enter the ratio value.

3. Step 3: Choose unit

   Select whether your angle is in degrees or radians.

4. Step 4: Calculate

   The calculator will provide the result with step-by-step explanation.

Tips, Assumptions & Limitations

• Remember that sin(0°) = 0, cos(0°) = 1, and tan(0°) = 0.
• For angles in radians, π radians = 180°.
• Inverse trigonometric functions return angles, not ratios.
• The range of arcsin is [-π/2, π/2] and arccos is [0, π].
• Cosecant, secant, and cotangent are undefined when their reciprocal functions equal zero.
• Use the calculator to verify your manual calculations and learn the step-by-step process.