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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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Find the exact value of each of the six trigonometric functions of \( \theta \), if \( (-2,-7) \) is a point on the terminal side of angle \( \theta \). \( \sin \theta=\square \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominator Find the exact value, if any, of the following composite function. Do not use a calculator. \( \cos ^{-1}\left[\cos \left(\frac{7 \pi}{10}\right)\right] \) Select the correct choice below and, if necessary, fill in the answer box within your choice. A. \( \cos ^{-1}\left[\cos \left(\frac{7 \pi}{10}\right)\right]= \) (Simplify your answer. Type an exact answer, using \( \pi \) as needed. Use integers or fractions for any numbers in the expression.) B. It is not defined. Find the exact value of each of the six trigonometric functions of \( \theta \), if \( (4,-2) \) is a point on the terminal side of angle \( \theta \). \( \sin \theta=\square \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) 47. Resolver " \( x \) " que satisface: \( 22^{\prime \prime} * \operatorname{Cos} x+\operatorname{Cos} 2 x=-\frac{3}{2}, 90^{\circ}<x<180^{\circ} \) \( \begin{array}{llll}\text { A) } 120^{\circ} & \text { B) } 135^{\circ} & \text { C) } 127^{\circ} & \text { D) } 143^{\circ} \\ \text { E) } 150^{\circ}\end{array} \) Establish the identity. \( \frac{4 \sec \theta}{\csc \theta}+\frac{2 \sin \theta}{\cos \theta}=6 \tan \theta \) Write the left side of the identity in terms of sine and cosine. Rewrite the numerator and denominator separately. Simplify the fraction from the previous step such that both the fractions have the common denominator cos \( \theta \). \( +\frac{2 \sin \theta}{\cos \theta} \) (Do not simplify.) The expression from the previous step then simplifies to 6 tan \( \theta \) using what? A. Addition and the Cancellation Property B. Addition and a Reciprocal Identity C. Addition and an Even-Odd Identity D. Addition and a Quotient Identity E. Addition and a Pythagorean Identity Find the exact value of each of the six trigonometric functions of \( \theta \), if \( (1,1) \) is a point on the terminal side of angle \( \theta \). \( \sin \theta=\square \) \( ( \) Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) Use a calculator to solve the equation on the interval \( 0 \leq \theta<2 \pi \). \( \cos \theta=-0.96 \) What are the solutions in the interval \( 0 \leq \theta<2 \pi \) ? Select the correct choice and fill in any answer boxes in your choice below. A. The solution set is \{ (Type your answer in radians. Round to two decimal places as needed. Use a comma to separate answers as needed.) B. There is no solution. Find the exact value of the following expression. \( \cos ^{-1}(-1) \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( \cos ^{-1}(-1)=\square \) (Simplify your answer. Type an exact answer, using \( \pi \) as needed. Use integers or fractions for any numbers in the expression.) B. The function is not defined. Use the triangle shown on the right and the given information to solve the triangle. \[ b=2, A=80^{\circ} \text {; find } a, c \text {, and } B \] \( \mathrm{a}=\square \) (Round to two decimal places as needed.) \( \mathrm{c}=\square^{\circ} \) (Round to two decimal places as needed.) \( \mathrm{B}=\square^{\circ} \) (Round to one decimal place as needed.) Use a calculator to find the value in radians of the following expression rounded to two decimal places. \( \sin ^{-1} 0.3 \) \( \sin ^{-1} 0.3=\square \) radian(s) (Type your answer in radians. Round to the nearest hundredth as needed.)
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