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.

This page introduces the fundamental concepts of trigonometry in relation to the coordinate plane. It covers the six trigonometric functions of the angle θ and their relationships.

The page begins by explaining the SOHCAHTOA mnemonic, which helps students remember the basic trigonometric ratios.

Definition: SOHCAHTOA stands for Sine = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, and Tangent = Opposite / Adjacent.

The document then provides examples of trigonometric values for common angles such as 30°, 45°, and 60°.

Example: For a 45° angle, sin 45° = cos 45° = √2/2, and tan 45° = 1.

The concept of co-functions is introduced, explaining the relationship between complementary angles.

Highlight: Co-functions are trigonometric functions of complementary angles. For example, sin θ = cos $90° - θ$.

The page also covers the distance formula and introduces the concept of reference angles.

Vocabulary: A reference angle is the acute angle formed between the terminal side of an angle and the x-axis.

Lastly, the page provides a visual representation of reference angles in all four quadrants of the coordinate plane.