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Home Question Bank Math Trigonometry Archive 2024 December 03

Trigonometry Questions from Dec 03,2024

Browse the Trigonometry Q&A Archive for Dec 03,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Use reference angles to find the exact value of the following expression. \( \cot \left(-\frac{\pi}{4}\right) \) Select the correct choice below and, if necessary, fill in the answer box to, complete your choice. A. \( \cot \left(-\frac{\pi}{4}\right)=\square \) (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expressi) the denominator.) B. The answer is undefined. Given that \( \sin \alpha=\frac{2}{3} \) and \( 90^{\circ}<\alpha<180^{\circ} \), find \( \sin 2 \alpha \) and \( \cos 2 \alpha \). \( \sin 2 \alpha=\square \quad \cos 2 \alpha=\square \) Use reference angles to find the exact value of the following expression. Do not use a calculator. \( \sin \left(-300^{\circ}\right) \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( \sin \left(-300^{\circ}\right)=\square \) (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the the denominator.) B. The answer is undefined. Given that \( \sin \alpha=\frac{4}{7} \) and \( 90^{\circ}<\alpha<180^{\circ} \), find \( \sin 2 \alpha \) and \( \cos 2 \alpha \). \( \sin 2 \alpha=\square \cos 2 \alpha=\square \) Write the following as a single sine or cosine function of an angle: \( \cos ^{4} 4 x-\sin ^{4} 4 x \) Use reference angles to find the exact value of the following expression. Do not use a calculator. \[ \begin{array}{l}\sin \left(-300^{\circ}\right) \\ \text { A. select the correct choice below and, if necessary, fill in the answer box to complete your choice. } \\ \text { (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions fo } \\ \text { the denominator.) } \\ \text { B. The answer is undefined. }\end{array} \] Use reference angles to find the exact value of the foliowing expresision \( \tan \frac{7 \pi}{3} \) Select the correct chaice below and if necessary, fill in the answer box to camptere your chotce A. \( \frac{7 \pi}{3}= \) Use reference angles to find the exact value of the following expression. Do not use a calculator. \( \csc \frac{5 \pi}{6} \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( \csc \frac{5 \pi}{6}=\square \) (Simplify your answer. Type an exact answer, usilig radicals as needed. Use integers or fractions for any numbers in the the denominator.) Use reference angles to find the exact value of the following expression. \( \cos \frac{7 \pi}{6} \) Select the correct choice below and, if necessary, fill in the answer box to gomplete your choice. A. \( \cos \frac{7 \pi}{6}=\square \) (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions the denominator.) 16 Use reference angles to find the exact value of the following expression. Do not use a calculator. \[ \begin{array}{l}\tan 780^{\circ} \\ \text { Select the correct choice below and, if necessary, fill in the answer box to complete your choice. } \\ \text { A. } \tan 780^{\circ}= \\ \text { (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any } n \\ \text { the denominator.) } \\ \text { B. The answer is undefined. }\end{array} \]
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