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