Math Problem Statement
(csc^2(-pi/4))/(-8sin(-pi/4))
Solution
Let's simplify the given expression:
Step-by-Step Solution:
-
Evaluate :
- Recall that .
- .
- Therefore, .
- Simplify to .
- So, .
-
Evaluate :
- As noted, .
-
Simplify the denominator :
-
Put it all together:
-
Simplify the fraction:
-
Rationalize the denominator:
Final Answer:
Would you like any further details or have questions on any steps?
Related Questions:
- How would you simplify without using negative angles?
- Can you explain why ?
- How do you rationalize a denominator, and why is it necessary?
- What is the general process for simplifying trigonometric expressions?
- How do the even-odd identities affect trigonometric functions?
Tip:
When working with trigonometric functions of negative angles, remember that and because sine is an odd function.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Trigonometric Identities
Simplification of Expressions
Formulas
csc(x) = 1/sin(x)
sin(-x) = -sin(x)
Rationalizing the denominator
Theorems
Odd-Even Function Theorem
Simplification of Trigonometric Functions
Suitable Grade Level
Grades 10-12
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