# Trigonometry Examples and Problem Solving

This page focuses on applying trigonometric concepts to solve problems. It provides **six trigonometric functions example problems with solutions**.

The first example demonstrates how to find the three main trigonometric functions (sine, cosine, and tangent) for an angle of 315°.

**Example**: For θ = 315°, the reference angle is 45°. Therefore, sin 315° = -√2/2, cos 315° = √2/2, and tan 315° = -1.

The second example illustrates how to solve a right triangle given the hypotenuse and one side.

**Highlight**: The Pythagorean theorem (a² + b² = c²) is crucial for solving right triangles in trigonometry.

The third example shows how to find all six trigonometric functions when given the sine value and the sign of cosine.

**Example**: Given sin θ = 5/13 and cos θ < 0, we can determine that cos θ = -12/13, tan θ = -5/12, csc θ = 13/5, sec θ = -13/12, and cot θ = -12/5.

The page concludes with a reminder of the SOHCAHTOA and CSCO (cosecant, secant, cotangent) mnemonics, reinforcing the relationships between the six trigonometric functions.

**Vocabulary**: CSCO stands for Cosecant = 1/Sine, Secant = 1/Cosine, and Cotangent = 1/Tangent.

This comprehensive guide serves as an excellent resource for students studying **trigonometry in the coordinate plane**, providing both theoretical explanations and practical problem-solving techniques.