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Hogar Banco de preguntas Matemáticas Trigonometría Archive 2025 January 20

Trigonometry Questions from Jan 20,2025

Browse the Trigonometry Q&A Archive for Jan 20,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Use a calculator to solve the equation on the interval \( 0 \leq \theta<2 \pi \). \( \sin \theta=0.52 \) 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. Use a calculator to solve the equation on the interval \( 0 \leq \theta<2 \pi \). \( \cos \theta=-0.8 \) 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. Solve the equation. Give a general formula for all the solutions. List six solutions. \[ \sin \theta=\frac{\sqrt{3}}{2} \] Identify the general formula for all the solutions to \( \sin \theta=\frac{\sqrt{3}}{2} \) based on the smaller angle, \( \theta=\square, k \) is an integer (Simplify your answer. Use angle measures greater than or equal to 0 and less than \( 2 \pi \). Type an exact answer, using \( \pi \) as needed. Use integers or fractions for any numbers in the expression. Type an expression using k as the variable.) Solve the equation on the interval \( 0 \leq \theta<2 \pi \). \( 2 \cos ^{2} \theta-\sqrt{3} \cos \theta=0 \) Select the correct choice and fill in any answer boxes in your choice below. A. The solution set is \( \{ \). \( \} \). (Simplify your answer. Type an exact answer, using \( \pi \) as needed. Type your answer in radians. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. There is no solution. Attendance at a state park throughout the year is found to be periodic and can be modeled by a sine function. The attendance ranges from a low of approximately \( 1,000,000 \) visitors in September to a high of approximately \( 2,000,000 \) visitors in March. If \( t \) is the month number, where \( t=1 \) is January, and \( N(t) \) is the attendance, in millions, of visitors, which of the functions can be used to model this behavior? \[ N(t)=0.5 \sin \left(\frac{\pi}{6} t\right)+1.5 \] \( N(t)=2 \sin \left(\frac{\pi}{6} t\right)-1 \) \( N(t)=1.5 \sin \left(\frac{\pi}{6} t\right)+0.5 \) \( N(t)=0.5 \sin (2 \pi t)+1.5 \) Solve the equation. \( 2 \sin ^{2} \theta-3 \sin \theta+1=0 \) What 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. A. The solution set is \{ \}. (Simplify your answer. Type an exact answer, using \( \pi \) as needed. Type your answer in radians. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. There is no solution. The pressure of a fluid flowing through a closed system, \( P \), after \( t \) seconds can be modeled by the function \( P(t)=100+30 \sin \left(\frac{12 \pi}{5} t\right) \). Answer parts (a) through (c) below. (a) In the interval \( [0,1] \), determine the times at which the pressure of the fluid is 100 mmHg . The solution set is \( \{0,0.42,0.83\} \). (Type an integer or decimal rounded to two decimal places as needed. Use a comma to separate answers as needed.) (b) In the interval \( [0,1] \), determine the times at which the pressure of the fluid is 130 mmHg . The solution set is \( \{\square\} \). (Type an integer or decimal rounded to two decimal places as needed. Use a comma to separate answers as needed.) What are the zeros of \( f(x)=12 \cos ^{2} x-3 \) on the interval \( [0,2 \pi] \) ? The zeros are (Type an exact answer in terms of \( \pi \). Use a comma to separate answers as needed.) Solve the equation. \[ (1-\cos \theta)=\sin ^{2} \theta \] What 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. A. The solution set is \( \{\square\} \). (Simplify your answer. Type an exact answer, using \( \pi \) as needed. Type your answer in radians. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. There is no solution. Solve the equation on the interval \( 0 \leq \theta<2 \pi \). \( 5 \sin ^{2} \theta-13 \sin \theta+8=0 \) What 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. A. The solution set is \{ \}. (Simplify your answer. Type an exact answer, using \( \pi \) as needed. Type your answer in radians. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. There is no solution.
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