Unit 3C Review
Flashcard
•
Mathematics
•
12th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the value of \( \sin^{-1}\left(-\frac{1}{2}\right) \)?
Back
The value is \( -\frac{\pi}{6} \).
2.
FLASHCARD QUESTION
Front
What are the intervals of \( \theta \) for \( [0, 2\pi) \) where \( 2\sin \theta + 1 < 0 \)?
Back
The intervals are \( (\frac{7\pi}{6}, \frac{11\pi}{6}) \cup (0, 2\pi) \).
3.
FLASHCARD QUESTION
Front
How do you simplify \( \cot x \sin x \sec^2 x \)?
Back
It simplifies to \( \sec x \).
4.
FLASHCARD QUESTION
Front
Which of the following is false: \( \sin(a+b) = \sin a \cos b - \cos a \sin b \)?
Back
This statement is false; the correct identity is \( \sin(a+b) = \sin a \cos b + \cos a \sin b \).
5.
FLASHCARD QUESTION
Front
How do you simplify \( \cos x - \cos x \sin^2 x \)?
Back
It simplifies to \( \cos^3 x \).
6.
FLASHCARD QUESTION
Front
What is the range of the inverse sine function \( \sin^{-1}(x) \)?
Back
The range is \( [-\frac{\pi}{2}, \frac{\pi}{2}] \).
7.
FLASHCARD QUESTION
Front
What is the Pythagorean identity involving sine and cosine?
Back
The Pythagorean identity is \( \sin^2 x + \cos^2 x = 1 \).
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