Precalculus Family Weekend

Trigonmetry

100

Complete the identity: ______ + 1 = cot^2 x

csc^2x

300

What would you find first in this problem, and what law would you use to find it? Solve triangle ABC given that a = 8, c = 5, and B = 40

b, using law of cosines

400

Evaluate arccos (-2)

not possible

Evaluate

100

log base 2 of 1/8

-3

200

ln e^7

7

300

sin pi

0

400

arccos (1)

0

500

arcsin (-1/2)

-pi/6

Equations

100

Solve on [0, 2pi): tanx = -1

x = 3pi/4, 7pi/4

200

Solve: 4^(x+3) = 16^(5x)

x=1/3

300

e^x + 5 = 66

x = 4.111

400

Solve: log base2 of (x+3) = 5

x=29

500

Solve on [0, 2pi): 2sin^2 x - 3sin x +1 =0

x = pi/6, 5pi/6, pi/2

Graphing

100

Is this graph of this function increasing or decreasing? f(x)=4^(-x)

decreasing (because equivalent to f(x)=(1/4)^x)

200

State the vertical asymptotes of this function: x / (x^2-3x+2)

x=2, x=1

300

State the horizontal asymptote of this function: (3x^2)/(x^3 - 4x +3)

y=0

Miscellaneous

100

State the domain of this function: (x^2 +2)/(2x^2 - 5x - 3)

R, x cannot equal -1/2, 3

200

Given that C=102.3^o, B=28.7^o, b = 27.4, find A

A = 49

500

State the period and amplitude of y=2tan(pi)(x)

Amplitude = 2, Period = 1