Section 1.2 Completed Notes: Precalculus Review, Unit Circle Trigonometry, Exponents and Logarithms

Flashcards covering slope and line equations, unit circle standard values, common trigonometric values at key angles, logarithms, and solving exponential equations using logarithms.

What is the slope formula for a line through points (x1, y1) and (x2, y2)?

(y2 - y1) / (x2 - x1)

What is the slope-intercept form of a line with slope m and y-intercept b?

y = mx + b

What is the point-slope form of the equation of a line with slope m through point (x1, y1)?

y - y1 = m(x - x1)

What is the general form of a line's equation?

Ax + By = C

What are the coordinates on the unit circle at angle 0, π/2, π, and 3π/2?

(1,0); (0,1); (-1,0); (0,-1)

What are the cosine and sine values at angle π/6 on the unit circle?

cos(π/6) = √3/2, sin(π/6) = 1/2

What are the cosine and sine values at angle π/4 on the unit circle?

cos(π/4) = sin(π/4) = √2/2

What are the cosine and sine values at angle π/3 on the unit circle?

cos(π/3) = 1/2, sin(π/3) = √3/2

In Quadrant II, what are the signs of cosine and sine?

Cosine is negative; sine is positive

What is a logarithm?

The inverse of an exponential; log_b(x) = y if b^y = x

What does ln(x) denote?

Natural logarithm (logarithm with base e)

State an exponent rule: a^m * a^n = ?

a^(m+n)

State another exponent rule: (a^m)^n = ?

a^(mn)

What is a^0?

1

What is a^(-m) equal to?

1 / a^m

How do you solve an exponential equation where the variable is in the exponent?

Take a logarithm of both sides (preferably natural log) and solve for the variable

If a^x = b, how do you solve for x using logarithms?

x = ln(b) / ln(a)