Given the right triangle below, use the sine function to write a trigonometric expression for the missing angle .
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
8. Trigonometric Functions on Right Triangles
Trigonometric Functions on Right Triangles
Multiple Choice
What is the positive value of D in the interval [0,2π) that will make the following statement true? Express the answer in four decimal places.
secD=3.2842
A
rad
B
rad
C
rad
D
rad
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Verified step by step guidance1
Understand that the problem is asking for the angle D in radians such that sec(D) = 3.2842, where D is in the interval [0, π/2).
Recall that the secant function is the reciprocal of the cosine function, so sec(D) = 1/cos(D). Therefore, we need to find D such that 1/cos(D) = 3.2842.
Rearrange the equation to find cos(D): cos(D) = 1/3.2842.
Use a calculator to find the angle D in radians by taking the inverse cosine (arccos) of the value obtained in the previous step: D = arccos(1/3.2842).
Ensure that the calculated angle D is within the specified interval [0, π/2). If it is not, adjust accordingly, but in this case, the angle should naturally fall within the interval.
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