PreCalc Chapter 4 Test

Question 0

One ______ is the measure of a central angle that intercepts an arc length to the radius of the circle

Answer 0

Radian

Question 1

Two angles that have the same initial and terminal sides are ________

Answer 1

Coterminal

Question 2

Two positive angles that have a sum of pi/2 are _____ angles, where two positive angles that have a sum of pi are ____ angles

Answer 2

Complementary, supplementary

Question 3

The angle measure that is equivalent to a rotation of 1/360 of a complete revolution about an angle’s vertex is one ________

Answer 3

Degree

Question 4

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

Answer 4

Linear, angular

Question 5

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 __________

Answer 5

A=1/2r^2theta

Question 6

A circle has an _____ number of symmetries

Answer 6

Infinite

It is the perfect 2D figure

Question 7

What is a radian?

Answer 7

An arch length (on the unit circle)

Question 8

How do you find Coterminal angles

Answer 8

+/-360 or 2pi(GET A COMMON DENOMINATOR IF YOU DO 2PI)

Question 9

How do you convert radians to degrees?

Degrees to radians?

Answer 9

Multiply by 180/pi

Multiply by pi/180

Question 10

One radian is approximately _____ degrees

Answer 10

60 (57.29)

Question 11

Arc length= ________________ where theta is measured in ______

Answer 11

S=rtheta, radians

Question 12

Linear speed=

Angular speed=

Answer 12

arc length/time
central angle (in radians)/time

Question 13

How much is one revolution for rotational speed

Answer 13

2pi radians

Question 14

A sector is _____

Answer 14

Part of a circle

Question 15

There are ______ minutes in one degree

Answer 15

60

Question 16

Each real number t corresponds to a point (X,y) on the ____ ______

Answer 16

Unit circle

Question 17

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

Answer 17

Periodic

Question 18

The smallest number c for which a function f is periodic is called the ______ of f

Answer 18

Period

Question 19

A function f is ________ when f(-t)=-f(t) and ______ when f(-t)=f(t)

Answer 19

Odd, even

Question 20

Sine is the _ value, cosines is the _ value, and tangent is the _ over the _ value

Answer 20

Y,X,Y,X

Question 21

______ and _____ functions are even, meaning that at -t, it is just t

Answer 21

Cosine, secant

Question 22

The ____, _____, _____, and ____ functions are odd, meaning at -t, it is -(sin)t

Answer 22

Sine, cosecant, tangent, cotangent

Question 23

Sin^2theta+_____^2theta=1
1+____^2theta=sec^2theta
1+cot^2theta=____^2theta

Answer 23

Cos, tan, csc

Question 24

The hypotenuse is never _____

Answer 24

Negative

Question 25

When taking the sine of a function in radians, make sure your calculator is in ______ mode

Answer 25

Radian

Question 26

Relative to the acute angle theta, the three sides of a right triangle are the ____ side, the _____ side, and the _______ side

Answer 26

Opposite, adjacent, hypotenuse

Question 27

Confunctions of _______ angles are equal

Answer 27

Complementary

Question 28

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 _______

Answer 28

Elevation, depression

Question 29

What is the difference between sin^2theta and sintheta^2

Answer 29

Square the sine, square the theta

Question 30

Angle of depression and angle of elevation are _______ for the same triangle

Answer 30

Equal

Question 31

You use trig values when you have ______ and you want to find ____
You use their inverses when you have ___ and you want to find ____

Answer 31

Angles, lengths

Lengths, angles

Question 32

Because r=square toot x^2+y^2 cannot be ____, the sine and cosine functions are _____ for any real value for theta

Answer 32

Zero, defined

Question 33

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’

Answer 33

Reference

Question 34

Always make sure to check your signs by asking yourself if tangent/cosine/sine/etc is +/- in quadrant ____

Answer 34

..

Question 35

How do you change revolutions to radians for angular speed

Answer 35

Just multiply by 2pi