Chapter 6: Q.86 (page 396)

use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator:
$\sec (- \frac{π}{18}) \cos (\frac{37 π}{18})$

Short Answer

Expert verified

The exact value of $\sec (- \frac{π}{18}) \cos (\frac{37 π}{18})$ is $1$

Step by step solution

Given information

We are given a expression $\sec (- \frac{π}{18}) \cos (\frac{37 π}{18})$

Use the periodicity of trigonometric function cos2π+θ=cosθ

We get

$\sec (- \frac{π}{18}) \cos (\frac{37 π}{18}) \sec (\frac{π}{18}) \cos (2 π + \frac{π}{18}) \sec (\frac{π}{18}) \cos (\frac{π}{18}) = \sec (\frac{π}{18}) \frac{1}{\sec (\frac{π}{18})} = 1$

Conclusion

The exact value of $\sec (\frac{π}{18}) \cos (\frac{37 π}{18}) i s 1 .$

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use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator:
$\sec (- \frac{π}{18}) \cos (\frac{37 π}{18})$

Short Answer

Step by step solution

Given information

Use the periodicity of trigonometric function cos2π+θ=cosθ

Conclusion

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use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator:sec-π18cos37π18

Short Answer

Step by step solution

Given information

Use the periodicity of trigonometric function cos2π+θ=cosθ

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Statistics

Decision Maths

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator:
$\sec (- \frac{π}{18}) \cos (\frac{37 π}{18})$