Math Problem Statement
What if I get: sec(-pi) how would I solve using add 2pi or subtract 2pi
Solution
To solve , you can use the periodicity of the secant function (a reciprocal of cosine) to simplify the angle by adding or subtracting . Here’s how you approach it:
Step-by-step solution:
-
Recall the periodicity of the secant function:
- The secant function is periodic with a period of , meaning .
-
Simplify using : To simplify within the standard interval , you can add to it: So, .
-
Evaluate : Recall that . From the unit circle:
- ,
- Hence, .
Final Answer:
Key Notes:
- Adding or subtracting simplifies the angle without changing the value of the trigonometric function.
- The result shows that .
Would you like me to provide further examples or details on using for simplifications?
Related Questions:
- What is the period of other trigonometric functions like sine, cosine, and tangent?
- How does secant relate to cosine, and what are its key properties?
- Can we use symmetry instead of to solve ?
- How do we evaluate secant for other common angles like or ?
- What happens if you’re given secant for negative angles in degrees instead of radians?
Tip:
Always reduce angles to a principal range (like for radians) to simplify trigonometric evaluations!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Trigonometry
Periodicity of Trigonometric Functions
Formulas
\( \sec(x) = \frac{1}{\cos(x)} \)
Periodicity: \( \sec(x + 2\pi) = \sec(x) \)
Theorems
Periodic properties of trigonometric functions
Reciprocal relationship between secant and cosine
Suitable Grade Level
Grades 9-12