PRE-CALC CHAPTER 4 (REVIEW) STUDY GUIDE
4.1
Define an angle using its parts: Vertex, Initial and Terminal side
Give the direction (CW or CCW) for a positive and negative angle
Define radian and state how many radians in a circle
State the four quadrants of the X-Y plane and the corresponding
angular values in terms of fractional 
Define the term acute, obtuse, coterminal, complementary and
supplementary angles
Convert from degrees to radians (decimal and fractions of ) and vice
versus
Calculate arc length and convert from arc length to theta
Convert from linear to angular speed and vice versus
4.2
Recognize that trig functions can be viewed as parametric functions
giving X and Y values in the X-Y plane using a unit circle
State the parametric definitions of the 6 trig functions (sine, cosine,
tangent, secant, cosecant, cotangent)
Define a periodic function and recognize the periodicity of the trig
functions
State the domain and range of the six trig functions
Given an angular value determine the 6 trig function values using a
calculator
State which trig functions are odd and even and describe that
meaning graphically
4.3
State the definitions of the 6 trig functions using right angle ratios
Give the values of the sine, cosine, and tangent of 0, 30, 45, 60, and
90 degrees from memory and given the sine, cosine, and tangent
values, give the corresponding angles in degrees and radians
State the equality of cofunctions of complementary angles
State the reciprocal and quotient identities
State the Pythagorean identities
Use the identities to solve problems involving multiple trig functions
Use degrees, minutes, and seconds on the calculator to give trig
function values to 6 digits of precision
Convert from degrees, minutes, and seconds to degrees.decimals
and vice versa
Use the calculator to give the angular values of an inverse trig
function’s ratio
Solve right triangle distance problems
4.4
State the definition of the 6 trig functions in terms of angle and R
Recognize the sign values of the 3 trig functions in the 4 quadrants
Define and determine the reference angle for a given angle
Determine the angle (in degrees and radians) given the value of any
of the 6 trig functions and given an angle determine the values of any
of the 6 trig functions in exact and approximate terms
4.5
Graph by hand the sine and cosine curves from the interval 0 to 2
and then by extension added periods
Define amplitude of a sine/cosine curve
Graph by hand the sine and cosine functions that have been
transformed by translation, amplitude, reflection, and period
4.6
Graph by hand the other 4 trig functions that have been transformed
by translation, amplitude, reflection, and period
Sketch the product of two functions, one involving the sine or cosine
function
4.7
Define the inverse of the 6 trig functions
Determine the value of an inverse trig function using the calculator
State the domain and range of the inverse functions
Sketch the graph of the 6 inverse functions
Use composite and inverse properties of the 6 functions
4.8
Solve distance problems involving the trig functions including vector
addition
Solve simple harmonic motion problems