Chapter 4.1-4.8 Test H Precalc
Range for arctan
(-π/2, π/2)
Radian—>Degree
180/π rad
The period of y = csc x is
2π
The area of a sector of a circle with radius r and central angle θ, where θ is measured in radians, is given by the formula ___.
A=(1/2)r^2θ
Circumference Formula
C = 2πr
One period of a sine or cosine is one ___________ of the sine or cosine curve
Cycle
The angle measure that is equivalent to a rotation of 1 of a complete revolution about an angle's vertex is one ________.
Degree
period
Distance it takes to complete a full cycle
An angle of _________ represents the angle from the horizontal upward to an object, whereas an angle of ___________ represents the angle from the horizontal downward to an object
Elevation, depression
For the function y = a sin(bx − c), b represents the ________ ________ of one cycle of the graph of the function.
Phase shift
For the function y = d + a cos(bx − c), d represents a ________ ________ of the basic curve.
Vertical shift
Range for arcsin
[-π/2, π/2]
Range for arccos
[0, π]
Match trig to right triangle definition: cosine
adj/hyp
Match trig to right triangle definition: cotangent
adj/opp
The range of y = sec x is ________.
all real except that y < (or equal to) 1 or y > (or equal to) 1
The __________ of a sine or cosine curve represents half the distance between the maximum and minimum values of the function
amplitude
Radian measures are...
arc lengths on the unit circle
A ________ measures the acute angle that a path or line of sight makes with a fixed north-south line.
bearing
Two positive angles that have a sum of π/2 are ________ angles, and two positive angles that have a sum of π are ________ angles.
complementary, supplementary
Two angles that have the same initial and terminal sides are ________.
coterminal
Interval
distance between critical values
The number of cycles per second of a point in simple harmonic motion is its ________
frequency
Match trig to right triangle definition: secant
hyp/adj
Match trig to right triangle definition: cosecant
hyp/opp
The ________ speed of a particle is the ratio of the arc length traveled to the elapsed time, and the ________ speed of a particle is the ratio of the change in the central angle to the elapsed time.
linear, angular
A function f is ___________ when f(-t) = -f(t) and _________ when f(-t) = f(t)
odd, even
The tangent, cotangent, and cosecant functions are ________, so the graphs of these functions have symmetry with respect to the ________.
odd, origin
Relative to the acute angle θ, the three sides of a right triangle are the ________ side, the ________ side, and the ________.
opp, adj, hyp
Match trig to right triangle definition: tangent
opp/adj
Match trig to right triangle definition: sine
opp/hyp
The smallest number c for which a function f is periodic is the ___________ of f
period
The time for one complete cycle of a point in simple harmonic motion is its ________.
period
A function f is ______________ when there exists a positive real number c such that f(t + c) =f(t) for all t is the domain of f.
periodic
The period of y = tan x is
pi/b
One ________ is the measure of a central angle that intercepts an arc equal in length to the radius of the circle.
radian
To sketch the graph of a secant or cosecant function, first make a sketch of its ________ function.
reciprocal
The acute angle formed by the terminal side of an angle θ in standard position and the horizontal axis is the ________ angle of θ and is denoted by θ′.
reference
What equation do you use to find arc lengths?
s=rθ
Pythagorean Identities
sin²∅ + cos²∅ = 1 tan²∅ + 1 = sec²∅ cot²∅ + 1 = csc²∅
Reference angle
the angle between the terminal side and the x-axis - always acute - any of the quadrants - positive
Each real number t corresponds to a point (x, y) on the ________ ________.
unit circle
The graphs of the tangent, cotangent, secant, and cosecant functions have ________ asymptotes.
vertical
The domain of y = cot x is all real numbers such that ________.
x ≠ n(pi)
45-45-90 triangle
x, x, x√2
30-60-90 Triangle
x, x√3, 2x
cos represents the
x-value
sin represents the
y-value
tan represents the
y-value/x-value
Degree—>Radian
π rad/180