Pre-Calculus Flashcards

Which expression equals log(AB)?

Answer: log A + log B

The product rule of logarithms states log(AB) = log A + log B.

If sin(θ) = 3/5 and θ is in the first quadrant, what is cos(θ)?

Answer: 4/5

Using the Pythagorean identity: cos(θ) = √(1 - sin²θ) = √(1 - 9/25) = √(16/25) = 4/5.

Solve: e^x = 7 (round to nearest hundredth)

Answer: x ≈ 1.95

Taking the natural log of both sides: x = ln(7) ≈ 1.946.

The graph of y = f(x - 2) is a shift of y = f(x) in which direction?

Answer: 2 units right

Replacing x with x - 2 shifts the graph 2 units to the right.

What is the value of tan(45°)?

Answer: 1

tan(45°) = sin(45°)/cos(45°) = (√2/2)/(√2/2) = 1.

How many solutions does 2sin(x) = 1 have on the interval [0, 2π)?

Answer: 2

sin(x) = 1/2 gives x = π/6 and x = 5π/6, two solutions in [0, 2π).