Multiple Choice
What is the exact value of ?
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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 that the sine function for special angles like 30°, 45°, and 60° can be found using the properties of an equilateral triangle or a 30°-60°-90° right triangle.
Consider an equilateral triangle with each side of length 2. By drawing an altitude, you split it into two 30°-60°-90° right triangles.
In a 30°-60°-90° triangle, the sides are in the ratio 1 : \(\sqrt{3}\) : 2, where 1 is the length opposite 30°, \(\sqrt{3}\) is opposite 60°, and 2 is the hypotenuse.
Since sine is defined as the ratio of the length of the side opposite the angle to the hypotenuse, write the expression for \(\sin\) 60^\(\circ\) as the opposite side over the hypotenuse: \(\sin 60^\circ = \frac{\sqrt{3}}{2}\).
This gives the exact value of \(\sin\) 60^\(\circ\) without using a calculator.
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