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Practice FINAL Math 112 Spring 2004
NAME:
- [5] TRUE/FALSE: Circle T in each of the following cases if the statement is always true. Otherwise, circle F. Let θ be a real number and k and integer.
T F sin(π 3 + x) = sin π 3 + x
T F csc(−θ) = − csc θ
T F eln(−1)^ = − 1
T F ln xy = ln x − ln y
T F If sin θ > 0 and cot θ < 0, then cos θ < 0
T F The domain of tan−^1 is [− 1 , 1]
T F The range of sin−^1 is [0, π]
T F If a + bi is a root of a polynomial, a − bi is also a root.
T F The conjugate to 2i + 3i^2 is 2i − 3 i^2
T F The remainder of 3x^112 − 6 x^3 + 2x − 1 when divided by x − 1, is 6
Show your work for the following problems. The correct answer with no
supporting work will receive NO credit.
- [2] Draw the complete graphs of sec x and cos−^1 y.
- [4] Evaluate: sin π 2 csc^2 π 6 − cot^2 π 6 csc^2 π 4
tan 4434 π cos − 3 π sec − 3 π
- [5] Evaluate:
sin−^1 (sin(sin−^1 (sin 34 π ))) sec(tan−1 3 4 ) sin(tan−^1 (−1) − π 4 )
- [1] Find a degree 3 polynomial with complex coefficients and with roots: 3, i, and 2 − i.
- [9] Let z = 1 + i and w = 1 − i
- Find (^) wz using regular (rectangular form).
- Find the polar form for z and w.
- Using polar form find z ∗ w
- Find z^8
- Find the 3rd roots of w
- [2] Given that a = 10
2, b = 20, and A = π 6 with the standard notation, determine if the information describes 0, 1, or 2 triangles and solve for them/it if they/it exist/s.
- [4] Draw the graph produced by: −3 sin(4θ − π)
- [3] Prove for all x in the domain: (Hint: use identities.)
sin^4 x − cos^4 x = 2 sin^2 x − 1
sin x − sin 2x cos 3x + cos x
= − tan x
