For each expression, identify which coterminal angle to use & determine the exact value of the expression.
Table of contents
- 0. Fundamental Concepts of Algebra3h 32m
- 1. Equations and Inequalities3h 27m
- 2. Graphs1h 43m
- 3. Functions & Graphs2h 17m
- 4. Polynomial Functions1h 54m
- 5. Rational Functions1h 23m
- 6. Exponential and Logarithmic Functions2h 28m
- 7. Measuring Angles40m
- 8. Trigonometric Functions on Right Triangles2h 5m
- 9. Unit Circle1h 19m
- 10. Graphing Trigonometric Functions1h 19m
- 11. Inverse Trigonometric Functions and Basic Trig Equations1h 41m
- 12. Trigonometric Identities 2h 34m
- 13. Non-Right Triangles1h 38m
- 14. Vectors2h 25m
- 15. Polar Equations2h 5m
- 16. Parametric Equations1h 6m
- 17. Graphing Complex Numbers1h 7m
- 18. Systems of Equations and Matrices3h 6m
- 19. Conic Sections2h 36m
- 20. Sequences, Series & Induction1h 15m
- 21. Combinatorics and Probability1h 45m
- 22. Limits & Continuity1h 49m
- 23. Intro to Derivatives & Area Under the Curve2h 9m
9. Unit Circle
Reference Angles
Multiple Choice
Identify what angle, θ , satisfies the following conditions.
sinθ=21; tanθ < 0
A
30°
B
150°
C
60°
D
300°
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Verified step by step guidance1
Recognize that the equation \( \sin\theta = \frac{1}{2} \) implies that \( \theta \) could be an angle where the sine value is \( \frac{1}{2} \). Common angles with this sine value are 30° and 150°.
Recall that the sine function is positive in the first and second quadrants. Therefore, the angles 30° and 150° are potential solutions.
Consider the condition \( \tan\theta < 0 \). The tangent function is negative in the second and fourth quadrants.
Since 30° is in the first quadrant where tangent is positive, it does not satisfy \( \tan\theta < 0 \).
150° is in the second quadrant where tangent is negative, thus satisfying both conditions: \( \sin\theta = \frac{1}{2} \) and \( \tan\theta < 0 \).
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