Chapter 4 math test

Coterminal angle rules quadrant 1

0<(theta)<(pie)/2

45-45-90

1/ 1 / x / x (square root 2) 1 / 1--------------/ x

30-60-90 triangle

1/ 1 / (all under square root) / x 3x/2 1 / 1--------------/ x/2

Degrees in radians

360= 2 pie rad 180= pie rad 1= pie/180 rad 1 rad= (180/pie)

Coterminal angle rules quadrant 4

3pie/2<theta<2pie

How do you find coterminal angles

Add or subtract 2(pie) because that is one revolution. Can change it to 12(pie)/6 or 8(pie)/4

Coterminal angles

Angles that have the same initial and terminal sides

Coterminal angle rules quadrant 2

Pie/2<theta<pie

Coterminal angle rules quadrant 3

Pie<theta<3pie/2

amplitude of sine and cosine curves

the amplitude of y = a sin x and y = a cos x represents half the distance between the maximum and minimum values of the function

why use reference angle

to determine the values of the trigonometric functions of angles greater than 90 degrees (or less than 0)

when graphing sec, cos, sin, csc what do you set the parenthesis equal to

zero and 2pie

domain and range of tan and cot

Tan: domain = all reals excluding 1/2 pie values range = negative infinity< y< infinity Cot: domain = all reals excluding whole pie values range = negative infinity< y< infinity

Radian

The measure of a central angle (theta) that intercepts an arc s equal in length to the radius r of the circle (Theta)=s/r

supplementary angles

angles that add to 180 degrees

Complementary angles

angles that add to 90 degrees

linear speed

consider a particle moving at a constant speed along a circular arc of radius r. If s is the length of the arc traveled in time t, then linear speed v of the particle is linear speed v = arc length/ time = s/t

arc length

for a circle of radius r, a central angle (theta) intercepts an arc length s give by where theta is measured in radians s=r(theta) ex: a circle has a radius of 4 inches, find the length of the arc intercepted by a central angle of 240 degrees 1. first convert 240 to radian measure = 4pie/3 radians 2. using a radius of r=4, find arc length s=4(4pie/3) = 16 pie/3 = 16.67 inches

angular speed

if theta is the angle (in radians) corresponding to the arc length s, then the angular speed w (omega) of the particle is angular speed w = central angle/ time = theta/t

period of sine and cosine curves

let b be a positive real number, the period of y = a sin bx and y = a cos bx is given by period = 2pie/ b

to convert degrees to radians

multiply degrees by pie rad/180 or go 360/(given degree) =x then take 2/x then make it a fraction and whatever it is simplified thats the radians with a pie on the numerator ex: 360/30 degrees = 12, then take 2/12=.16666667, make fraction (1/6), so answer is 1pie/6

to convert radians to degrees

multiply radians by 180/pie rad

when graphing tan what do you set the parenthesis equal to

negative pie/ 2 and positive pie/ 2

when graphing cot what do you set the parenthesis equal to

pie and zero

reference angles

the acute angle theta prime (O') formed by the terminal side of theta and the horizontal axis -so its only within the quadrant, not the whole circle!