Math Problem Statement
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Solution
To solve the given problem, we are provided with:
Steps:
-
Understand the Quadrant:
Since and , the angle is in the second quadrant (where sine is positive, and cosine is negative). -
Find using the Pythagorean identity:
Recall the identity: Substituting : Therefore: Since (in the second quadrant): -
Check (if needed):
Using :
Final Answer:
Do you want details on any step, or have any questions?
Related Questions:
- What are the values of , , and ?
- How does the quadrant affect the signs of trigonometric functions?
- Can we solve this problem using a unit circle approach?
- How is the Pythagorean identity derived?
- How do we verify these results graphically?
Tip:
When determining signs of trigonometric functions, always consider the quadrant using the ASTC rule (All Students Take Calculus).
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Pythagorean Identity
Quadrants in Trigonometry
Formulas
Pythagorean Identity: sin^2(θ) + cos^2(θ) = 1
tan(θ) = sin(θ) / cos(θ)
Theorems
Pythagorean Theorem
ASTC Rule (All Students Take Calculus)
Suitable Grade Level
Grades 10-12
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