MS 101 Alg & Trig test four • 27 June 2014 Name:

1. __________ Calculate 462 sin(90°)
2. __________ Calculate 462 cos(90°)
3. __________ Calculate 462 sin(45°)
4. __________ Calculate 462 cos(45°)
5. __________ Calculate 462 tan(45°)
6. __________ Calculate 462 sin(30°)
7. __________ Calculate 462 cos(30°)
8. __________ Calculate 462 tan(30°)
9. Calculate the six Scalable Vector Graphics (SVG) coordinates for a "north pointing" hexagon inscibed in a circle with a radius of 462 pixels. In the diagram the angle θ is 30°. The coordinates should be given in the SVG coordinate system.
   
   
   
   Wave equation in terms of wavelength λ and distance x: $y=\mathrm{a}sin\left(\frac{2\mathrm{\pi }x}{\mathrm{\lambda }}\right)$
   Wave equation in terms of period τ and time t: $y=\mathrm{a}sin\left(\frac{2\mathrm{\pi }t}{\mathrm{\tau }}\right)$
   Period τ and frequency f relationship: $\mathrm{\tau }=\frac{1}{f}$
10. A RipStik lays down a wave according to the equation: $y=8sin\left(\frac{2\mathrm{\pi }x}{39}\right)$
    1. a = _______________ Write the amplitude a of the equation.
    2. λ = _______________ Write the wavelength λ of the equation.
11. A spring oscillates vertically according to the equation: $y=25sin\left(\frac{2\mathrm{\pi }t}{1.4}\right)$
    1. a = _______________ Write the amplitude a of the equation.
    2. τ = _______________ Write the period τ of the equation.
    3. f = _______________ Calculate the frequency f of the equation.
12. A RipStik was swizzled across a large sheet of paper. The swizzle wave can be seen in the diagram.
    
    1. ________ How many waves are shown in the diagram?
    2. λ = _______________ Write the wavelength λ
    3. a = _______________ Write the amplitude a.
    4. τ = _______________ Write the period τ.
    5. f = _______________ Calculate the frequency f.
    6. y = ______ sin( _________ x). Write out the equation of the wave in terms of the wavelength λ and distance x.
13. Sketch a graph of the following function: $y=30sin\left(\frac{2\mathrm{\pi }x}{6}\right)$