Questions and Answers
What is the exact value of csc 135 degrees?
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What is the value of sec $ rac{3 ext{π}}{2}$?
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What are the graphs of y = sin x and y = csc x in the interval from -2π to 2π?
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What is the estimated value of sec 165 degrees, rounded to the nearest tenth?
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What is the length of the rafters needed for a roof where the angle is 19 degrees?
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Study Notes
Reciprocal Trigonometric Functions
- Cosecant (csc) of 135 degrees equals √2, indicating a defined value.
- Secant (sec) of 3π/2 is undefined, highlighting a vertical asymptote in the function's graph.
Graph Behavior
- The graphs of y = sin x and y = csc x between -2π to 2π exhibit periodic behavior with sin x oscillating and csc x having vertical asymptotes where sin x equals zero.
Estimating Values Using Graphs
- Secant (sec) of 165 degrees can be estimated using its graph, yielding a result of approximately -1 when rounded to the nearest tenth.
Practical Application of Cosecant Function
- The length of rafters necessary for a rain shelter is modeled by the function y = 4 csc(θ), where the peak height is 4 feet.
- For an angle θ of 19 degrees, the required length of the rafters calculates to 12.3 feet, rounding the value to the nearest tenth.
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Description
This quiz covers the reciprocal trigonometric functions as explored in Algebra 2B Unit 7, Lesson 7. It includes finding exact values, evaluating expressions, and analyzing the graphs of sine and cosecant functions. Prepare to test your understanding of these concepts with various flashcards.
