Figure 10.1 should remind you of trigonometric functions you've seen before. Which of the following functions is most directly represented by the coordinates of a point on the unit circle at an angle from the positive x-axis?
Table of contents
- 0. Review of College Algebra4h 45m
- 1. Measuring Angles40m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
3. Unit Circle
Trigonometric Functions on the Unit Circle
Multiple Choice
What is the value of on the unit circle?
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Verified step by step guidance1
Recall that the tangent function on the unit circle is defined as \(\tan \theta = \frac{\sin \theta}{\cos \theta}\), where \(\theta\) is the angle in radians.
Identify the angle given: \(\theta = \frac{\pi}{3}\). This corresponds to 60 degrees, a common special angle in trigonometry.
Recall the sine and cosine values for \(\frac{\pi}{3}\): \(\sin \frac{\pi}{3} = \frac{\sqrt{3}}{2}\) and \(\cos \frac{\pi}{3} = \frac{1}{2}\).
Substitute these values into the tangent formula: \(\tan \frac{\pi}{3} = \frac{\sin \frac{\pi}{3}}{\cos \frac{\pi}{3}} = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\).
Simplify the fraction by dividing the numerators and denominators accordingly to find the exact value of \(\tan \frac{\pi}{3}\).
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