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 the definition of the tangent function in terms of sine and cosine: \(\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}\).
Identify the angle given: \(\theta = \frac{\pi}{3}\). This is a special angle commonly found on the unit circle.
Recall the exact values for sine and cosine at \(\frac{\pi}{3}\): \(\sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}\) and \(\cos\left(\frac{\pi}{3}\right) = \frac{1}{2}\).
Substitute these values into the tangent formula: \(\tan\left(\frac{\pi}{3}\right) = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\).
Simplify the fraction by dividing the numerators and denominators: \(\tan\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2} \times \frac{2}{1} = \sqrt{3}\).
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