1. What is a Trigonometric Equation?

A trigonometric equation is an equation involving trigonometric functions (sine, cosine, tangent, etc.) of a variable. Solving such equations helps find angles that satisfy given trigonometric conditions.

2. How Does the Calculator Work?

The calculator solves basic trigonometric equations of the form:

Where:

• trig function — sin, cos, or tan
• value — A number between -1 and 1 for sin/cos, any real number for tan
• x — The angle to be found (in degrees or radians)

Explanation: The calculator uses inverse trigonometric functions to find the principal value solution.

3. Importance of Trigonometric Equations

Details: Trigonometric equations are fundamental in mathematics, physics, engineering, and many applied sciences. They help solve problems involving periodic phenomena, waves, and circular motion.

4. Using the Calculator

Tips: Select the trigonometric function, enter the value (must be valid for the selected function), and choose the unit for the solution (degrees or radians).

5. Frequently Asked Questions (FAQ)

Q1: Why does my calculator only give one solution?
A: The calculator returns the principal value. Trigonometric equations typically have infinitely many solutions that can be found by adding multiples of the period.

Q2: What are the valid input ranges?
A: For sin and cos, values must be between -1 and 1. For tan, any real number is valid.

Q3: How do I find all solutions?
A: For sin(x)=a, solutions are x = arcsin(a) + 360°n and x = 180° - arcsin(a) + 360°n (n∈ℤ). Similar patterns exist for cos and tan.

Q4: What's the difference between degrees and radians?
A: Degrees and radians are different units for measuring angles. 360° = 2π radians. The choice depends on the context.

Q5: Can this solve more complex equations?
A: This calculator handles basic forms. More complex equations may require algebraic manipulation before solving.