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

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MATH 115 QUIZ 5 SOLUTIONS December, 2016 Instructor: S. Sands 1. (6 pts) The note 'A' below the note 'middle C' is a sound wave with ordinary frequency f = 220 Hertz = 220 cycles/second. State a sinusoid which models this note, assuming that the amplitude is 1 and the phase 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 equation sing4666g1876g4667 tang4666g1876g4667 + uni221A3 sing4666g1876g4667 = 0 , finding all solutions in the interval [0, 360 ° ). Show work . HINT: Note that sin( x ) is a factor. (You should be able to provide the exact values of the solutions and state them in degrees.) [Section 10.7] °
(chart on page 724 is a helpful reference; for tangent look for ratio of y / x = −uni221A3 ) °
3. (8 pts) Solve the equation 4 arccosg46665g1876g4667 = 3g2024 . Find the exact value(s). HINT: Write an appropriate corresponding equation involving sine. Show work. . [Section 10.7]
4. (10 pts) Solve the equation sing46662g1876g4667 + uni221A2 cosg4666g1876g4667 = 0 , finding all solutions in the interval [0, 2 π ). Show work. HINT: Start by applying an appropriate trig identity. (You should be able to provide the exact values of the solutions and state them in radians.) [Section 10.7] π π
5. (12 pts) For the triangle ABC , we are given that B = 80 ° , a = 52.0, and b = 78.0. (Side a is the side opposite angle A , side b is the side opposite angle B , and side c is the side opposite angle Solve 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 .)