Tema
Q:
4. \( \tan t+2 \cos t \csc t=\sec t \csc t+\cot t \)
Q:
In which quadrant would \( \theta \) be if \( \sin \theta=-\frac{\sqrt{3}}{2} \) and \( \cos \theta>0 \) ? (1 point)
Quadrant IV
Quadrant I
Quadrant II
Quadrant III
Q:
In which quadrant would \( \theta \) be if \( \tan \theta=\frac{\sqrt{3}}{3} \) and \( \cos \theta=-\frac{\sqrt{3}}{2} ? \) (1 point)
Quadrant II
Quadrant IV
Quadrant III
Quadrant I
Q:
Determine the sign of \( \cos \left(\frac{5 \pi}{3}\right) \) and the quadrant in which it lies. (1 point)
\( \cos \left(\frac{5 \pi}{3}\right) \) is positive and lies in Quadrant IV.
\( \cos \left(\frac{5 \pi}{3}\right) \) is negative and lies in Quadrant IV.
\( \cos \left(\frac{5 \pi}{3}\right) \) is negative and lies in Quadrant III.
\( \cos \left(\frac{5 \pi}{3}\right) \) is positive and lies in Quadrant I.
Q:
If \( \tan \theta=\frac{\sqrt{3}}{3} \), which of the following is a possible coordinate pair?
(1 point)
\( \left(-\frac{\sqrt{3}}{2}, \frac{1}{2}\right) \)
\( \left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right) \)
\( \left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right) \)
\( \left(-\frac{1}{2},-\frac{\sqrt{3}}{2}\right) \)
Q:
What is the value of \( \tan \theta \) in this 45-45-90 triangle?
(1 point)
1
\( \frac{\sqrt{2}}{2} \)
\( \frac{\sqrt{2}}{\frac{\pi}{4}} \)
Q:
Which of the following is the correct ratio for \( \tan \left(\frac{2 \pi}{3}\right) \) ? (1 point)
\( \tan \left(\frac{2 \pi}{3}\right)=\frac{-\frac{n}{2}}{-\frac{1}{2}}=\sqrt{3} \)
\( \tan \left(\frac{2 \pi}{3}\right)=\frac{-\frac{\sqrt{2}}{2}}{\frac{1}{2}}=-\sqrt{3} \)
\( \tan \left(\frac{2 \pi}{3}\right)=\frac{-\frac{1}{2}}{\frac{\sqrt{3}}{2}}=-\frac{\sqrt{3}}{3} \)
\( \tan \left(\frac{2 \pi}{3}\right)=\frac{\frac{\sqrt{2}}{2}}{-\frac{1}{2}}=-\sqrt{3} \)
Q:
Which of the following is not a solution for \( \cos \theta=0 \) ? (1 point)
\( 2 \pi \)
\( -\frac{\pi}{2} \)
\( \frac{3 \pi}{2} \)
\( \frac{\pi}{2} \)
Q:
What is the domain of \( \sin \theta \) ? (1 point)
\( \begin{array}{l}-\pi \leq x \leq \pi \\ -2 \pi \leq x \leq 2 \pi \\ -\infty<x<\infty \\ 0 \leq x \leq 2 \pi\end{array} \)
Q:
Which of the following mathematical expressions is equivalent to \( \cos 60^{\circ} \) ? (1 point)
\( \sin \frac{\pi}{3} \)
\( \cos \frac{\pi}{3} \)
\( \cos \frac{\pi}{6} \)
\( \sin \frac{\pi}{4} \)
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