MATH 115 Quiz 5 Explanation - MATH 115 QUIZ 5 SOLUTIONS...

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MATH 115 QUIZ 5 SOLUTIONSDecember, 2016Instructor: S. Sands1. (6 pts) The note 'A' below the note 'middle C' is a sound wave with ordinary frequencyf= 220 Hertz= 220 cycles/second. State a sinusoid which models this note, assuming that the amplitude is 1 and thephase shift is 0.(no explanation required) [section 11.1, p. 881 and exercise 11.1, #1]g1845g4666g1872g4667 = g1827 sing4666g2033g1872 + g2030g4667
2. (10 pts) Solve the equationsing4666g1876g4667 tang4666g1876g4667 + uni221A3sing4666g1876g4667 = 0, finding all solutions in theinterval [0, 360°).Show work.HINT: Note that sin(x) is a factor.(You should be able to provide the exactvalues of the solutions and state them in degrees.) [Section 10.7]°
(chart on page 724 is a helpful reference; for tangentlook for ratio ofy/x=−uni221A3)°
3. (8 pts) Solve the equation4 arccosg46665g1876g4667 = 3g2024. Find the exact value(s). HINT: Write an appropriatecorresponding equation involving sine.Show work..[Section 10.7]
4. (10 pts) Solve the equationsing46662g1876g4667 + uni221A2cosg4666g1876g4667 = 0, finding all solutions in the interval [0, 2π).Show work.HINT: Start by applying an appropriate trig identity.(You should be able to provide the exactvalues of the solutions and state them in radians.)[Section 10.7]ππ
5. (12 pts) For the triangleABC, we are given thatB= 80°,a= 52.0, andb= 78.0.(Sideais the side opposite angleA, sidebis the side opposite angleB, and sidecis the side opposite angleSolve the triangle; that is, find the two remaining angles and the remaining side.Report angles to the nearest degree and the length rounded to the nearest tenth.Show work.C.)

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