MS 101 Alg & Trig test five ⬠ Name:

01 July 2011

1. ________ Calculate arcsin(0.5), report the result in degrees.
2. ________ Calculate $\arccos \left(\frac{\sqrt{3}}{2}\right)$, report the result in degrees.
3. __________ For a right triangle with an adjacent side of length 65 and an opposite side of 72, find the angle θ in degrees.
4. __________ For a right triangle with an adjacent side of length 65 and an opposite side of 72, find the length of the hypotenuse r.
5. __________ For a right triangle with an adjacent side of length 80 and a hypotenus of 82, find the angle θ in degrees.
6. __________ For a right triangle with an adjacent side of length 80 and a hypotenuse of 82, find the length of the opposite side y.
7. ______, _____ Find the other two numbers in a Pythagorean triple where one of the three numbers is 7.
8. 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.
9. _____________________ Simplify (sin x + cos x)². Use the first answer obtained.
10. _________ Determine whether is an identity or not: $\frac{1}{\sin \left(\mathrm{x}\right)\sec \left(\mathrm{x}\right)}=\cos \left(\mathrm{x}\right)\csc \left(\mathrm{x}\right)$
11. _________ Determine whether is an identity or not: $\frac{1}{\sin \left(x\right)\tan \left(x\right)}=\cos \left(x\right)\cot \left(x\right)$
12. __________ Looking over the WolframAlpha output for the above problem, are there values of x for which the two sides of the equals sign are equal? If yes, what are those values of x? __________, ________