Which of the following represents the polar equation as a rectangular equation?
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
Which of the following expressions has the same value as ?
A
B
C
D
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Verified step by step guidance1
Recall the definition of the tangent function for negative angles: \(\tan(-\theta) = -\tan(\theta)\). So, \(\tan(-45^\circ) = -\tan(45^\circ)\).
Evaluate \(\tan(45^\circ)\) using the known value: \(\tan(45^\circ) = 1\). Therefore, \(\tan(-45^\circ) = -1\).
Check each given expression to see which one equals \(-1\) by using known trigonometric values and identities:
For example, \(-\cos(180^\circ)\): since \(\cos(180^\circ) = -1\), then \(-\cos(180^\circ) = -(-1) = 1\), which is not equal to \(-1\).
Similarly, analyze \(\tan(45^\circ)\), \(\cot(135^\circ)\), and \(-\sin(270^\circ)\) by recalling their values or using identities to find which matches \(-1\).
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