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.
