PreCalc Chapter 4 Test Flashcards
One ______ is the measure of a central angle that intercepts an arc length to the radius of the circle
Radian
Two angles that have the same initial and terminal sides are ________
Coterminal
Two positive angles that have a sum of pi/2 are _____ angles, where two positive angles that have a sum of pi are ____ angles
Complementary, supplementary
The angle measure that is equivalent to a rotation of 1/360 of a complete revolution about an angle’s vertex is one ________
Degree
The _____ speed of a particle is the ratio of the arc length to the time traveled, and the _____ speed of a particle is the ratio of the central angle to the time traveled
Linear, angular
The area A of a sector of a circle with radius R and central angle theta, where theta is measured in radians, is given by the formula __________
A=1/2r^2theta
A circle has an _____ number of symmetries
Infinite
It is the perfect 2D figure
What is a radian?
An arch length (on the unit circle)
How do you find Coterminal angles
+/-360 or 2pi(GET A COMMON DENOMINATOR IF YOU DO 2PI)
How do you convert radians to degrees?
Degrees to radians?
Multiply by 180/pi
Multiply by pi/180
One radian is approximately _____ degrees
60 (57.29)
Arc length= ________________ where theta is measured in ______
S=rtheta, radians
Linear speed=
Angular speed=
arc length/time central angle (in radians)/time
How much is one revolution for rotational speed
2pi radians
A sector is _____
Part of a circle
There are ______ minutes in one degree
60
Each real number t corresponds to a point (X,y) on the ____ ______
Unit circle
A function f is ___ when there exists a positive real number c such that f(t+c)=f(t) for all t in the domain of f
Periodic
The smallest number c for which a function f is periodic is called the ______ of f
Period
A function f is ________ when f(-t)=-f(t) and ______ when f(-t)=f(t)
Odd, even
Sine is the _ value, cosines is the _ value, and tangent is the _ over the _ value
Y,X,Y,X
______ and _____ functions are even, meaning that at -t, it is just t
Cosine, secant
The ____, _____, _____, and ____ functions are odd, meaning at -t, it is -(sin)t
Sine, cosecant, tangent, cotangent
Sin^2theta+_____^2theta=1
1+____^2theta=sec^2theta
1+cot^2theta=____^2theta
Cos, tan, csc
The hypotenuse is never _____
Negative
When taking the sine of a function in radians, make sure your calculator is in ______ mode
Radian
Relative to the acute angle theta, the three sides of a right triangle are the ____ side, the _____ side, and the _______ side
Opposite, adjacent, hypotenuse
Confunctions of _______ angles are equal
Complementary
An angle that measures from the horizontal upward to an object is called the angle of _______, whereas the angle that measures from the horizontal downward to an object is called the angle of _______
Elevation, depression
What is the difference between sin^2theta and sintheta^2
Square the sine, square the theta
Angle of depression and angle of elevation are _______ for the same triangle
Equal
You use trig values when you have ______ and you want to find ____
You use their inverses when you have ___ and you want to find ____
Angles, lengths
Lengths, angles
Because r=square toot x^2+y^2 cannot be ____, the sine and cosine functions are _____ for any real value for theta
Zero, defined
The acute positive angle formed by the terminal side of an angle theta and the horizontal axis is called the ______ angle of theta and is denoted by theta’
Reference
Always make sure to check your signs by asking yourself if tangent/cosine/sine/etc is +/- in quadrant ____
..
How do you change revolutions to radians for angular speed
Just multiply by 2pi
