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Home Question Bank Math Trigonometry Archive 2024 November 05

Trigonometry Questions from Nov 05,2024

Browse the Trigonometry Q&A Archive for Nov 05,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Without using a calculator, compute the sine and cosine of \( \frac{4 \pi}{3} \) by using the reference angle. What is the reference angle? radians. In what quadrant is this angle? \( \sin \left(\frac{4 \pi}{3}\right)=\square \) \( \cos \left(\frac{4 \pi}{3}\right)=\square \) (Type sqrt(2) for \( \sqrt{2} \) and sqrt(3) for \( \sqrt{3} \).) Find the exact value. \[ \begin{array}{l}\sin \frac{-5 \pi}{6} \\ \text { Type }+ \text { or - } \\ {[?] \frac{\square]}{\square]}}\end{array} \] Find the exact value. \[ \begin{array}{c}\sin \frac{5 \pi}{2} \\ {[?]}\end{array} \] Without using a calculator, compute the sine and cosine of \( \frac{4 \pi}{3} \) by using the reference angle. What is the reference angle? \( \sin \left(\frac{4 \pi}{3}\right)=\square \) radians. \( \cos \left(\frac{4 \pi}{3}\right)=\square \) (answer \( 1,2,3 \), or 4) (Type sqrt(2) for \( \sqrt{2} \) and sqrt(3) for \( \sqrt{3} \).) Without using a calculator, compute the sine and cosine of \( 315^{\circ} \) by using the reference angle. What is the reference angle? In what quadrant is this angle? \( \sin \left(315^{\circ}\right)=\square \) degrees. \( \cos \left(315^{\circ}\right)=\square \) answer 1, 2, 3, or 4) (Type sqrt(2) for \( \sqrt{2} \) and sqrt(3) for \( \sqrt{3} \).) The point \( P \) is on the unit circle. If the \( y \)-coordinate of \( P \) is \( \frac{2}{7} \), and \( P \) is in quadrant II, then \( x=\square \) Submit Question Suppose \( m \angle A=\frac{3 \pi}{4} \) radians. Then \( \angle A \) is an angle in Quadrant One Two Three Four The reference angle for \( \angle A \) is \( \square \) radians. Leave your answer in terms of \( \pi \). Suppose \( m \angle A=\frac{7}{6} \pi \) radians. Then \( \angle A \) is an angle Quadrant in One Two Three Four The reference angle for \( \angle A \) is Suppose \( m \angle A=285 \) degrees. Then \( \angle A \) is an angle Quadrant in One Two Three Four The reference angle for \( \angle A \) is Given the reference angle \( \hat{\theta}=41^{\circ} \) find the measure of \( \theta \) in standard position if its terminal side lies in: (a) quadrant I: (b) quadrant II: (c) quadrant III: (d) quadrant IV:
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