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# Trigonometric Function Simplification and Values This document appears to be a worksheet or a set of notes covering trigonometric functions. It includes examples and exercises focused on simplifying trigonometric expressions and finding values of trigonometric functions for specific angles. The...

# Trigonometric Function Simplification and Values This document appears to be a worksheet or a set of notes covering trigonometric functions. It includes examples and exercises focused on simplifying trigonometric expressions and finding values of trigonometric functions for specific angles. The examples demonstrate methods for using trigonometric identities to simplify expressions, including expressions involving sine, cosine, and tangent functions. There is also a question about finding values where the trigonometric expressions are not allowed. **Example 2:** Find the exact values for `cos(2θ)` and `sec(2θ)` where `π ≤ θ ≤ 3π/2` and `cos(θ)` is a given value. This also includes intermediate steps required to derive the final result. **Example 3:** a) Simplify the expression `(1 - cos(θ))/sin(θ)` to a single primary trigonometric function. b) Find the values of θ where the expression `(1 - cos(θ))/sin(θ)` is undefined (non-permissible values.) The document also shows handwritten calculations and diagrams, likely supporting the understanding of the trigonometric transformations and simplification techniques and a diagram of a triangle.