## EXPLORATION 2 Evaluating Trigonometric Functions of

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

## EXPLORATION 2 Evaluating Trigonometric Functions of 60∘\mathbf{6 0}^{\circ} (1) Find the values of all six trigonometric functions for an angle of 60∘60^{\circ}. Note that most of the preliminary work has been done in Example 2. (2) Compare the six function values for 60∘60^{\circ} with the six function values for 30∘30^{\circ}. What do you notice? (3) We will eventually learn a rule that relates trigonometric functions of any angle with trigonometric functions of the complementary angle. (Recall from geometry that 30∘30^{\circ} and 60∘60^{\circ} are complementary because they add up to 90∘90^{\circ}.) Based on this exploration, can you predict what that rule will be? [Hint: The "co" in cosine, cotangent, and cosecant actually comes from "complement."]

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