1. The note 'G' above the note 'middle C' is a sound wave with ordinary frequency f= 392 Hertz = 392 cycles/second. State a sinusoid which models this note, assuming that the amplitude is 1 and the phase shift is 0. (no explanation required) 2. Solve the equation cos(2x) = /3 cos(x): finding all solutions in the interval [0. 2x). Show work. (You should be able to provide the exact values of the solutions and state them in radians.) 3. Solve the equation 4 arcsin( 2x) = 3x. Show work. 4. Solve the equation sin( x) tan(x) + ~/2 sin( x) =0, finding all solutions in the interval [0. 360). Show work. HINT: Start by factoring the left side of the equation, noting that sin x is a factor. (You should be able to provide the exact values of the solutions and state them in degrees.)5. For the triangle ABC, we are given that C: T5\8. Two hikers leave the same tent at a campground and go separate ways. One hiker wallts 3 miles directly south to Ashyille, and the other hilrer wall-ts 14 miles directly northwest I[i.e.= N45 \"Wj to Eellville. (Assume that the terrain is at.) How far apart are Ashville and Bellville [by the most direct route}? Show 1Vrk. (You may nd it very helpful to draw a picture, butyou do not need to submit it.) Round your answer to the nearest tenth of a mile. 9. lm airplane proceeds at a hearing of SETH: ying at 5413 miles per hour. @ explanations required) {a} State the angle 5' in standard position which corresponds to the hearing SEUGE. Us} Find the easterly and southerly components of the airplane's velocity. That is= nd the component form of the vector which has a magnitude of 54'] and makes the angle Ewith the positive xaJ-tis. {Use the value of 5' you stated in part (a).] State the exact values ggdglsg giye approximations to the nearest mile per hour. 10. Let E = {4,2} E1 1? = {1, 3). (Work required only for parts d and e, on the next page.) (a) Find T-I'ii 3E and state the result in component form. {b} State the exact magnitude (length) of i5 and the exact magnitude of E. (c) State the dot product ii - E. {d} Find pt'oj;f ii] in component form. Give exact values. Show work. (e) Determine the angle between iiand E. Show work. Write the exact angle as the arccosine of an appropriate number. Also, use a calculator to approximate the value of the angle: rounding the result to the nearest degree