MS 101 Alg & Trig test five 06 July 2012 Name:

1. A RipStik was swizzled across a large sheet of paper. The swizzle wave can be seen in the diagram below.
   
   
   λ = _______________ Write the wavelength λ of the RipStik swizzle wave in centimeters.
2. a = _______________ Calculate the amplitude a of the RipStik swizzle wave.
3. τ = _______________ Calculate the period τ of the RipStik swizzle wave.
4. b = _______________ Given that $b=\frac{2\pi }{\tau }$ , calculate b
5. y = ______ sin( _________ x). Given the general form y = a sin(bx) and the results above, write the equation for the RipStik swizzle wave.
6. τ = _______________ A tuning fork has a frequency of 256 Hertz. Calculate the period τ for the tuning fork.
7. x = __________ For a Pythagorean triple right triangle with a hypotenus of 17, find the length of the longer leg x.
8. y = __________ For a Pythagorean triple right triangle with a hypotenus of 17, find the length of the shorter leg y. Remember: this is a Pythagorean triple triangle.
9. θ = __________ For a Pythagorean triple right triangle with a hypotenus of 17, find the angle θ in degrees between the hypotenuse and the longer leg.
10. φ = __________ For a Pythagorean triple right triangle with a hypotenus of 17, find the angle φ in degrees between the hypotenuse and the shorter leg.
11. A Turkish F-4 Phantom II RC-4 is flying 23 kilometers off the coast of Syria. An anti-aircraft turret on the Syrian coast is tracking the Phantom. Write the equation for the angle θ as a function of the distance x along the coast and the distance (23) of the Phantom from the shore.
    θ =
12. x = __________. Solve solve cos²(x) + 8 cos(x) = 9 for x.
13. x = __________. Tougher: Solve cos²(x) + 8 cos(x) = 9 for 2 < x < 8.
14. _________ The equation for a projectile is given by:
    $\text{distance d}=\frac{2v^2\sin \left(\text{θ}\right)\cos \left(\text{θ}\right)}{\mathrm{9.8}}$
    For a velocity v of 14 m/s, and an angle of 30°, calculate the distance d.
15. _________ Solve for the velocity v:
    $\frac{2v^2\sin \left(30°\right)\cos \left(30°\right)}{\mathrm{9.8}}=\mathrm{80}$
16. _________ Solve for the angle x:
    19.6 sin(x) cos(x) = 9.8
    Report the angle x in radians for the solution between 0 and π/2.
17. A system demonstrating harmonic motion will be demonstrated at the front of the classroom. The instructor will provide data based on measurements of the system. Write the trigonometric function for the periodic system using the sine function, your calculation of the amplitude, and your calculation of the period.