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Questions and Answers
What is the exact value of csc 135 degrees?
What is the exact value of csc 135 degrees?
D.squared 2
What is the value of sec $ rac{3 ext{Ï€}}{2}$?
What is the value of sec $ rac{3 ext{Ï€}}{2}$?
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What are the graphs of y = sin x and y = csc x in the interval from -2Ï€ to 2Ï€?
What are the graphs of y = sin x and y = csc x in the interval from -2Ï€ to 2Ï€?
A
What is the estimated value of sec 165 degrees, rounded to the nearest tenth?
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?
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 3Ï€/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 -2Ï€ to 2Ï€ 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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