Solve Trig Equations Calculator

Trigonometric Equation Formula:

\[ \sin(\theta) = value \]

Principal Solution (θ):

All Solutions (0°-360°):

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1. What is a Trig Equations Calculator?

Definition: This calculator solves basic trigonometric equations of the form sin(θ)=value, cos(θ)=value, or tan(θ)=value.

Purpose: It helps students and professionals find angle solutions to trigonometric equations quickly and accurately.

2. How Does the Calculator Work?

The calculator uses inverse trigonometric functions:

\[ \theta = \sin^{-1}(value) \text{ or } \cos^{-1}(value) \text{ or } \tan^{-1}(value) \]

Explanation:

For sin(θ)=value, solutions are θ and 180°-θ
For cos(θ)=value, solutions are θ and 360°-θ
For tan(θ)=value, solutions are θ and θ+180°

3. Using the Calculator

Steps:

Select the trigonometric function (sin, cos, or tan)
Enter the value (must be between -1 and 1 for sin/cos)
Click Calculate to see solutions

4. Important Notes

For sin and cos functions, input values must be between -1 and 1
Tan function accepts any real number
Solutions are given in degrees between 0° and 360°
Principal solution is the angle returned by the inverse function

5. Frequently Asked Questions (FAQ)

Q1: Why are there multiple solutions?
A: Trigonometric functions are periodic, so there are infinitely many solutions. We show all unique solutions between 0° and 360°.

Q2: What if I get an error message?
A: For sin and cos, ensure your value is between -1 and 1. For tan, any real number is valid.

Q3: How are the solutions calculated?
A: We use inverse trig functions (arcsin, arccos, arctan) and apply trigonometric identities to find all solutions.

Q4: Can I get solutions in radians?
A: This calculator currently provides solutions in degrees only.

Q5: What about other trig functions (csc, sec, cot)?
A: These can be calculated as reciprocals (e.g., csc(θ)=1/sin(θ)), but are not directly supported in this version.