Math Problem Statement
Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is in the correct mode.) sec 11𝜋/8
Solution
To evaluate , we follow these steps:
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Recognize that . So we need to compute first.
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Ensure that the calculator is in radian mode since the angle is in terms of .
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Compute .
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Take the reciprocal of that value to find .
Now, let's calculate it:
Using a calculator:
So, the value of is approximately -2.6131.
Would you like further clarification or details?
Here are 5 related questions for further exploration:
- What is the sine of ?
- How would you evaluate ?
- Can you explain the difference between degrees and radians in trigonometry?
- What is the secant of , and how does it compare to ?
- How do you determine the quadrant in which lies?
Tip: Always double-check that your calculator is in the correct mode (radians or degrees) when working with trigonometric functions to avoid incorrect results!
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Radians
Secant Function
Cosine Function
Formulas
sec θ = 1 / cos θ
cos(θ) for angles in radians
Theorems
Reciprocal Identity: sec θ = 1 / cos θ
Unit Circle and Quadrant Analysis
Suitable Grade Level
Grades 9-12