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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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1) Simplify: \( \cos 2 u \cos 7 u-\sin 2 u \sin 7 u \) a) \( \cos 9 u \) b) \( \cos 5 u \) c) \( \sin 9 u \) d) \( \sin 5 u \) Let \( \theta \) be an angle in standard position. Name the quadrant in which \( \theta \) lies. \[ \begin{array}{l}\tan \theta>0, \sin \theta<0 \\ \text { The angle } \theta \text { lies in which quadrant? } \\ \text { in } \\ \text { in }\end{array} \] Let \( \theta \) be an angle in standard position. Name the quadrant in which \( \theta \) lies. \( \cos \theta<0, \csc \theta>0 \) The angle \( \theta \) lies in which quadrant? II I et \( \theta \) be an angle in standard position. Name the quadrant in which \( \theta \) lies. \( \sin \theta>0, \tan \theta<0 \) The angle \( \theta \) lies in which quadrant? II III IV Evaluate the following trigonometric function at the quadrantal angle, or state that the expression is undefined. \( \tan \pi \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( \tan \pi=\square \) B. \( \tan \pi \) is undefined. Evaluate the trigonometric function at the quadrantal angle, or state that the expression is undefined. \( \cot \pi \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( \cot \pi=\square \) B. The expression is undefined. Evaluate the following trigonometric function at the quadrantal angle, or state that the expression is undefined. \( \csc \frac{3 \pi}{2} \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The value of \( \csc \frac{3 \pi}{2} \) is B. \( \csc \frac{3 \pi}{2} \) is undefined. Evaluate the following trigonometric function at the quadrantal angle, or state that the expression is undefined. \[ \csc \frac{3 \pi}{2} \] Evaluate the following trigonometric function at the quadrantal angle, or state that the expression is undefined. \( \cos \pi \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The value of \( \cos \pi \) is B. \( \cos \pi \) is undefined. Solve the equation. \[ 6-6 \sin \theta=4 \cos ^{2} \theta \] A. The solution set is \( \{ \) the solution in the interval \( 0 \leq \theta<2 \pi \) ? Select the correct choice and fill in any answer boxes in your choice below. (Simplify your answer. Type an exact answer, using \( \pi \) as needed. Type your answer in radians. Use integers or fractions for any to separate answers as needed.) B. There is no solution.
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