Textbook Question
Find each exact function value. See Example 3.
tan 5π/3
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3. Unit Circle
Common Values of Sine, Cosine, & Tangent
Multiple Choice
What is the exact value of ?
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Verified step by step guidance1
Recall the special angles in trigonometry, particularly the 30°-60°-90° right triangle, which helps determine exact trigonometric values without a calculator.
In a 30°-60°-90° triangle, the sides are in the ratio 1 : \(\sqrt{3}\) : 2, where the side opposite 30° is 1, opposite 60° is \(\sqrt{3}\), and the hypotenuse is 2.
Since sine of an angle is defined as the ratio of the length of the side opposite the angle to the hypotenuse, write the formula: \(\sin(60^\circ) = \frac{\text{opposite side}}{\text{hypotenuse}}\).
Substitute the known side lengths for 60°: the opposite side is \(\sqrt{3}\) and the hypotenuse is 2, so \(\sin(60^\circ) = \frac{\sqrt{3}}{2}\).
Thus, the exact value of \(\sin(60^\circ)\) is expressed as \(\frac{\sqrt{3}}{2}\), which matches the correct answer.
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