PreCalc Chapter 4 Test Flashcards Preview

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Flashcards in PreCalc Chapter 4 Test Deck (36)
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0
Q

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

A

Radian

1
Q

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

A

Coterminal

2
Q

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

A

Complementary, supplementary

3
Q

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

A

Degree

4
Q

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

A

Linear, angular

5
Q

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

A=1/2r^2theta

6
Q

A circle has an _____ number of symmetries

A

Infinite

It is the perfect 2D figure

7
Q

What is a radian?

A

An arch length (on the unit circle)

8
Q

How do you find Coterminal angles

A

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

9
Q

How do you convert radians to degrees?

Degrees to radians?

A

Multiply by 180/pi

Multiply by pi/180

10
Q

One radian is approximately _____ degrees

A

60 (57.29)

11
Q

Arc length= ________________ where theta is measured in ______

A

S=rtheta, radians

12
Q

Linear speed=

Angular speed=

A
arc length/time
central angle (in radians)/time
13
Q

How much is one revolution for rotational speed

A

2pi radians

14
Q

A sector is _____

A

Part of a circle

15
Q

There are ______ minutes in one degree

A

60

16
Q

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

A

Unit circle

17
Q

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

A

Periodic

18
Q

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

A

Period

19
Q

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

A

Odd, even

20
Q

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

A

Y,X,Y,X

21
Q

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

A

Cosine, secant

22
Q

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

A

Sine, cosecant, tangent, cotangent

23
Q

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

A

Cos, tan, csc

24
Q

The hypotenuse is never _____

A

Negative

25
Q

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

A

Radian

26
Q

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

A

Opposite, adjacent, hypotenuse

27
Q

Confunctions of _______ angles are equal

A

Complementary

28
Q

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 _______

A

Elevation, depression

29
Q

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

A

Square the sine, square the theta

30
Q

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

A

Equal

31
Q

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

A

Angles, lengths

Lengths, angles

32
Q

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

A

Zero, defined

33
Q

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’

A

Reference

34
Q

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

A

..

35
Q

How do you change revolutions to radians for angular speed

A

Just multiply by 2pi