PreCalc Chapter 4 Test Part 3 Flashcards
A point that moves on a coordinate line is said to be in simple ______ ______ when its distance is d from the origin at time t is given by either d=asinwt or d=acoswt.
Harmonic motion
A _____ measures the acute angle that a path or line of sight makes with a fixed north-south line
Bearing
The time for one complete cycle of a point in simple harmonic motion is its ____________
Period
The number of cycles per second of a point in simple harmonic motion is its _________
Frequency
Angle of depression and angle of elevation are (equal/reciprocals) for the same triangle
Equal
A bearing is a _________ that always starts with (N or S/ E or W)
Direction, N or S
How is N75E spoken
75 degrees east of north
In a bearing, start at ________ and rotate towards the line
North or south
In a simple harmonic motion question, what are the rules for each variable
W is greater than 0, take absolute value of a, period=2w/pi, and opposite for frequency, frequency is measured in cycles per unit of time
If there is no direction on the bearing,_________________……
Degrees rotate clockwise from due North
Shadows are ________ unless stated otherwise
Horizontal
In a story problem, if angles of depression are given, what should you do
Put them in the triangles, making them angles of elevation
To find an equation of L in terms of h, make sure ____=________
L,h
Do bearings always start at the origin?
No- for example, if you are south east and you are looking to take a bearing towards the origin, start where you are, and go North west
Make sure to include ____ with period and frequency
Units
For regular figures inscribed in circles, the angle is always measured in the ____. Split an isosceles triangle using an _________ and multiply your final distance by ____
Center, amplitude, 2
When you are finding the least positive value, make sure your number is _____ 0
Greater than
Y=arcsinx,
What is alternative notation? What is the domain? Range?
Y=sin^-1x, [-1,1], [-pi/2,pi/2]
Y=cos^-1x,
What is the function? What is the domain? Range?
Y=arccosx, [-1,1], [0,pi]
Y=arctanx,
What is the alternative notation? Domain? Range?
Y=tan^-1x, [R’s], (-pi/2,pi/2)
Without restrictions, no trigonometric function has an ______ function
Why
Inverse,
Because the parent graph will not be one-to-one, making the inverse function fail Vertical Line Test
True of false, the arctanx=arcsinx/arccosx
False, if you plug in 1 for X, you get
Pi/4= pi/2 / 0
Y=arcsinx
Identify parts
Y is an angle, X is a length
What is the difference between y=arcsinx and y=sin^-1x
Arcs only have on solution (know range constraint), while inverse sine has infinite solutions
Arcsin and arctan of a negative length=a _________ angle
Negative
When doing the arccos(-0.41), make sure your calculator is in ______ mode
Radian
How do you do sin[arctan-5]
Build a triangle making your tangent -5 (watch constraint, in this case you’d build in quad 4), then use Pythagorean theorem to find your hypotenuse, and find the sine of theta
(3x)^2=
9x^2
