Topic 1
angles that share the same initial and terminal side (found by adding/subtracting 360 or 2pi)
coterminal angles
when a ray is on the positive x-axis (initial side), the other ray is what?
terminal side/angle
positioning in which the vertex is at the origin and one side touches the positive x-axis
standard position
unit of angle where the radius and the arc length of an angle are the same
radians
common unit of angle measurement denoted by a circle
degrees
the rate at which a full cycle is completed in a sinusoidal function (2pi/time)
angular frequency
a sine or cosine function with periodic oscillations
sinusoidal function
1. find amplitude (a)
2. find the period (2pi/b) and plot it
3. divide the period by 4 to find the distance between points
4. plot the first point by using the k value to shift up or down
5. plot the max and min points with the distance you found earlier
steps to graphing trig functions
equalities involving trig functions (such as pythagorean, reciprocal, double-angle, half-angle, sum and difference, law of sines, law of cosines)
trigonometric identities
cosA=1/secA secA=1/cosA
tanA=1/cotA cotA=1/tanA
reciprocal trig functions
using the ratio of the sides to find the angle
sin-1=arcsinx
cos-1=arccosx
tan-1=arctanx
inverse trig functions
when the angles of given trig functions are complementary (such as sin and cos), they are what?
cofunctions
when the angle of a trig ratio is 2x
sin2x=2sinxcosx
cos2x=cos^2x=sin^2x = 2cos^2x-1 = 1-2sin^2x
tan2x=(2tanx)/(1-tan^2x)
Double-angles
in which the angle of a trig ratio is divided in half
sinx/2 = +/- sqrt(1-cosx/2)
cosx/2 = +/- sqrt(1+cosx/2)
tanx/2 = +/- sqrt(1-cosx/1+cosx)
Half-angles
value of a trig function that's exact and not rounded (such as the values on the unit circle)
exact value
value that is close to the real value and usually rounded by a certain decimal places
approximate value
rise/run
slope
straight line that touches the curve of another line once
tangent line
straight line that intersects a curve at two points
secant line
(y2-y1)/(x2-x1)
average rate of change
slope of the secant line
(or distance traveled/time passed)
average velocity
points scattered on a graph that can show the relationship between the dependent and independent variables
scatter plot
used to find whether there is an existing relationship between a set of points
regression equation
rate at which the y is changing in terms of x, also the same as the slope of the tangent line
instantaneous rate of change
free points
free points