STUDY GUIDE-TRIG IDS

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•
Mathematics
•
12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Define the Pythagorean Identity in trigonometry.
Back
The Pythagorean Identity states that for any angle \( \theta \), the following holds: \( \sin^2 \theta + \cos^2 \theta = 1 \).
2.
FLASHCARD QUESTION
Front
What is the definition of \( \tan \theta \)?
Back
The tangent of an angle \( \theta \) is defined as the ratio of the opposite side to the adjacent side in a right triangle, or \( \tan \theta = \frac{\sin \theta}{\cos \theta} \).
3.
FLASHCARD QUESTION
Front
Simplify the expression: \( \frac{\csc^2 \alpha}{1 + \cot^2 \alpha} \)
Back
The simplified expression is \( 1 \).
4.
FLASHCARD QUESTION
Front
What is the relationship between \( \sec \theta \) and \( \cos \theta \)?
Back
The secant of an angle \( \theta \) is the reciprocal of the cosine: \( \sec \theta = \frac{1}{\cos \theta} \).
5.
FLASHCARD QUESTION
Front
Simplify the expression: \( \frac{-1}{\tan^2 N} + \frac{\sec^2 N}{\tan^2 N} \)
Back
The simplified expression is \( 1 \).
6.
FLASHCARD QUESTION
Front
What is the definition of \( \csc \theta \)?
Back
The cosecant of an angle \( \theta \) is defined as the reciprocal of the sine: \( \csc \theta = \frac{1}{\sin \theta} \).
7.
FLASHCARD QUESTION
Front
Simplify the expression: \( \tan \sigma + \frac{\sec \sigma}{\csc \sigma} \)
Back
The simplified expression is \( 2 \tan \sigma \).
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