Math 3 Final Exam

Sum of Interior Angles

(n-2) x 360

Interior angle of a polygon

(n-2) x 180 / 360

Sum of exterior angles

360

Exterior Angle of polygon

360/n

Change of base formula

log_b a = log a / log b

Logarithm equation

log_b Y = X

What is the common log

Log base 10

Properties of Logarithms

log_b (xy) = log_b x + log_b y

log_b x/y = log_b x - log_b y

log_b x^y = y * log_b x

log_b 1 = 0

log_b B = 1

b^log_bx = x

What must you always do when solving log equations?

Check for extraneous solutions

Area of a circle

A = πr²

Circumference

C = 2πr

Area of a sector

Theta/360 x πr²

Arc Length

Theta/360 × 2πr

Linear Velocity

LS = radius x angle (must be in radians) / time

Angular Speed

AS = angle (must be in radians) / time

Conversion from Degrees to Radians

Angle in degrees x π/180 = angle in radians

Angle in radians x 180/π = angle in degrees

Equation of a circle

(x - h)² + (y - k)² = r²

(h,k) is the center & r is the radius

General equation of a circle

Ax² + By² +Cx + Dy + E = 0

30,60,90 triangle

Angle across from 90 degrees (hypotenuse) = 2x

Angle across from 30 degrees (smallest side) = x

Angle across from 60 degrees = x square root of 3

45,45,90 triangle

Both angles across from 45 degrees = x

Angle across from 90 degrees (hypotenuse) = x square root of 2