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Hogar Banco de preguntas Matemáticas Trigonometría 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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The point given below is on the terminal side of an angle \( e \). Find the exact value of eachy of the six trigonometric functions of \( \theta \). \( (-24,10) \) \( \sin \theta=\square \) (Simplify your answer. Type an exact answer, using radicals as noeded. Use integens or fractions for any numbers in the expression. Rationalize all denominators.) The angle of inclination from the base of skyscraper A to the top of skyscraper B is approximately \( 10.7^{\circ} \). If skyscraper B is 1433 fee Assume the bases of the two buildings are at the same elevation. The distance from skyscraper A to skyscraper B is (Round to two decimal places as needed.) Two sides and an angle are given below. Determine whether the given information results in one triangle, two triangles, or no triangle at all. So \( \mathrm{b}=8, \mathrm{c}=7, \mathrm{~B}=100^{\circ} \) Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Type an integer or decimal rounded to two decimal places as needed.) A. A single triangle is produced, where \( \mathrm{C} \approx \square^{\circ}, \mathrm{A} \approx \square^{\circ} \), and \( \mathrm{a} \approx \square \). B. Two triangles are produced, where the triangle with the smaller angle C has \( \mathrm{C}_{1} \approx \square^{\circ}, \mathrm{A}_{1} \approx \square^{\circ} \), and \( \mathrm{a}_{1} \approx \square \), and the triangle with C. No triangles are produced. : Given \( \sin \theta=\cos \frac{3 \pi}{11} \) and \( \theta \in\left(\frac{\pi}{2}, \pi\right) \), find the exact value of \( \theta \) A triangular plot of land has one side along a straight road measuring 336 feet. A second side makes a \( 39^{\circ} \) angle with the road, and the third How long are the other two sides? The longer side of the triangular plot is \( \square \) feet. The shorter side of the triangular plot is \( \square \) feet. (Round to the nearest hundredth as needed.) Rewrite \( \frac{\cos \theta+\sin \theta}{\sin \theta}+\frac{\sin \theta-\cos \theta}{\cos \theta} \) over a common denominator. Type your answer in terms of sine and/or cosine. \( \frac{\cos \theta+\sin \theta}{\sin \theta}+\frac{\sin \theta-\cos \theta}{\cos \theta}=\square \) (Simplify your answer.) Solve the equation on the interval \( 0 \leq \theta<2 \pi \). \[ \begin{array}{l}\sin \theta+3=5 \\ \text { What are the solutions in the interval } 0 \leq \theta<2 \pi \text { ? Select the correct choice and fill in any answer boxes in your choice below. } \\ \text { A. The solution set is }\{\text {. } \\ \text { (Simplify your answer. Type an exact answer, using } \pi \text { as needed. Type your answer in radians. Use integers or fraction } \\ \text { to separate answers as needed.) } \\ \text { B. There is no solution. }\end{array} \text {. } \] Calcular " \( x \) " si: \( \cos \left(2 x+25^{\circ}\right) \csc \left(x+20^{\circ}\right)=1 \) \( \begin{array}{lll}\text { a) } 5^{\circ} & \text { b) } 10^{\circ} & \text { c) } \\ 15^{\circ} & \text { e) } 25^{\circ}\end{array} \) Solve the equation on the interval \( 0 \leq 0<2 \pi \) \[ (\tan 0-1)(\cos \theta+1)=0 \] Select the correct choice below and rill in any answer boxes in your choice. A. The solution set is (Simplify your answer. Type an oxact answer, using \( \pi \) as needed. Type your answer in radians. Use integers or B. There is no solution on this interval. Calcular " \( x^{\prime \prime} \) Si: \( \operatorname{sen}\left(2 x-14^{\circ}\right) \csc \left(x+5^{\circ}\right)=1 \) \( \begin{array}{ll}\text { a) } 13^{\circ} & \text { b) } 15^{\circ}\end{array} \) \( 17^{\circ} \) d) \( 19^{\circ} \)
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