Question

Help pleasse

Answer 1

do you remember the degrees to radians / the radians to degrees formulas from before?

Answer 2

1 degree is 0.01745329

Answer 3

well, I guess that works, but the answer they're probably looking for is to multiply by a specific conversion factor (to get a more precise answer)

Answer 4

so they're probably looking for something along the lines of "multiply the measurement by ____" where the appropriate conversion factor goes into the blank

the advantage to using this method is that, since we use pi instead of a truncated decimal, we retain the precision of the measurement

Answer 5

I hope that makes sense, lmk if you're having trouble understanding or if you want to move on to part III :S

Answer 6

Obviously I am going to rephrase this, but like this?

Answer 7

I don't think you need all of that, you just need to explain that you would multiply by the conversion factor

Answer 8

for I and II

Answer 9

the fluff at the bottom was just me explaining why we use these conversion factors instead of 1 degree = 0.01745329

it just needs to be "multiply by ___" [put the conversion factor into the blank]

Answer 10

multiply by 0.01745329

Answer 11

remember what I said earlier - that is technically correct but we would not want to use this as the conversion because we lose significant digits/accuracy

Answer 12

^ use this as your reference

Answer 13

Wouldn/t this be the answer like the formula

Answer 14

let's translate the first line into English

radians = (pi/180) * degrees

^ this means that, to convert from degrees to radians, we would multiply the angle measurement by pi/180, make sense?

Answer 15

Yes

Answer 16

so, for part I, we would write "to convert from degrees to radians, we would multiply the degree measurement by pi/180 degrees"

can you try repeating this process/logic for part II, using the appropriate conversion factor?

Answer 17

to convert from radians to degrees , we would divide the degree measurement by pi/180 degrees

Answer 18

^ keep in mind the conversion factor is not pi/180 for part II, it would be 180 degrees/pi

Answer 19

to convert from radians to degrees , we would divide the radians measurement by 180 degrees/pi

Answer 20

that's a multiplication sign, not a division sign ^_^

Answer 21

to convert from radians to degrees , we would multiply the radians measurement by 180 degrees/pi

Answer 22

awesome, that's it for parts I and II

Answer 23

for part III - any ideas/thoughts so far? can you think of any formula(s) for arc length and what the conditions are to use them?

Answer 24

2π rad=360°=400 gr

Answer 25

f we use degree: if the central angle is y degree, 2*pi*R*y/360 is the length of the arc

Answer 26

remember this one? we've used it a few times before, do you remember what must be true to use this? it has something to do with theta

Answer 27

If you measure the central angle in degress, you use the proportion circumference / 360° = length of arc / central angle in degrees,and if you measure the angle in radians, you use the proportion circumference / (2π) = length of arc / central angle in radians

Answer 28

(sorry if this is taking a while I'm just thinking of a good way to explain this ;_;)

Answer 29

Why are you apologizing, it's me duh i apologize that i am potentially stressing you out

Answer 30

so, what you posted is getting on the right track - the arc length is a function of the central angle and circumference, but units ~are~ important, since the units of central and the units of the arc must be consistent. for ex. if the angle is in radians the arc must also be in radians, likewise for degrees

Answer 31

Okay so the unit would be incorporated as well

Answer 32

yeah ^^" in short it does matter, it influences what formula you use and influences what units the end result will be in

Answer 33

SO this for Part III (of course rephrased) : the arc length is a function of the central angle and circumference, but units are important, since the units of central and the units of the arc must be consistent.

Answer 34

yeah, that's how I'd do it, I hope your teacher finds that acceptable :S

Answer 35

I'm sure she will ^~^

Answer 36

no calculators allowed, so we'll have to use the unit circle + our knowledge of equivalent angles

for 17pi/6, you can subtract multiples of 2pi (so 2pi, 4pi, etc.) until you get a value that is within the unit circle (0 to 2pi)

then you just need to read off the correct value from the Unit Circle

Answer 37

https://www.google.com/imgres?imgurl=https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/2000px-Unit_circle_angles_color.svg.png&imgrefurl=https://en.wikipedia.org/wiki/Unit_circle&h=2000&w=2000&tbnid=RQFx8m5rh-zcdM:&tbnh=160&tbnw=160&docid=vaD60PNNVCDhHM&usg=__FPt47P0wD7ZiUNUdZXqRBdEUA9I=&sa=X&ved=0ahUKEwiEnuruotPNAhUT6GMKHVC9DccQ9QEIIzAA

Answer 38

I would use this right

Answer 39

yes

if we subtract 2 pi from 17pi/6 what do we get?

Answer 40

5pi/6

Answer 41

awesome, so A would be 5pi/6 as the equivalent angle, then for B you would just use the Unit Circle to find sin(5pi/6)

Answer 42

1/2

Answer 43

awesome! so B is 1/2

Answer 44

for part II we just repeat a similar set of steps, first we would subtract multiples of 2pi from 13pi/4 until we get an angle btwn 0 and 2pi

Answer 45

okay part II A

Answer 46

SO this so far right

Answer 47

yup perfect

Answer 48

any ideas for the angle on part IIA?

Answer 49

Ugh no

Answer 50

to determine an equivalent angle, we just need to subtract 2 pi, until we get an angle btween 0 and 2pi

so 13pi/4 - 2pi = ?

Answer 51

5pi/4

Answer 52

awesome, so 5pi/4 is your angle for part A and then use the unit circle to find tan(5pi/4) for part B

Answer 53

1

Answer 54

awesome, so that's part IIB

Answer 55

similar process for part IIIC, first subtract 11pi/3 - 2pi

Answer 56

** part IIIA

Answer 57

5pi/3

Answer 58

good, then for B calculate sec(5pi/3) using the U.C. where sec = 1/cos

Answer 59

2

Answer 60

awesome, is that it or is there a part IV

Answer 61

that's it , but for this question. Are you busy or can you do more

Answer 62

yeah sure I can do a few more

Answer 63

they want you to use sin and angle (25) so set up the function

sin(theta) = opposite/hypotenuse, using angle 25 as theta, then find (b)

Answer 64

sin(theta) = opposite/hypotenuse,
sin(25)

Answer 65

good, but would you fill in for opposite/hypotenuse judging by the picture?

Answer 66

b/25

Answer 67

awesome so sin(25) = b/25 solve for b, round to 2 decimal places

Answer 68

10.57

Answer 69

awesome, so that's part I

for part II we have 2 sides + the hypotenuse, so we would just plug a, b, and the hypotenuse into pythagorean theorem to find a

Answer 70

10.57^2+25^2

Answer 71

hypotenuse goes on the right side

a^2 + (10.57)^2 = 25^2, solve for a

Answer 72

22.67

Answer 73

22.66 (since 22.6556 rounds to 22.66)

Answer 74

Part I: Triangle ABC is called a special right triangle. What kind of special right triangle is it (2 points)


Part II: Triangle BCD is also a right triangle. What is the measure of angle BCD (2 points)


Part III: Complete the sentence below.

In a 30-60-90 right triangle, the length of the hypotenuse is ________ times the length of the short leg, and the length of the long leg is _______ times the length of the short leg. (4 points)


Part IV: Using what you know about these special triangles, calculate the length of side BC. Show your work in words or equations. (4 points)



Part V: Use your knowledge about the relationship between side lengths of this triangle to find the length of side AC. Show your work in words or equations. (4 points)


Part VI: Find the length of the hypotenuse of triangle ABC (side AB). Show your work in words or equations. (4 points)


5. Imagine you are looking for a certain angle whose cosine is positive and whose sine is negative.
Part I: Name the two quadrants in which cosine is positive. (2 points)


Part II: Name the quadrants in which sine is negative (2 points)


Part III: Use the information in parts a and b to identify the quadrant in which cosine is positive and sine is negative. (2 points)


Part IV: Write down one angle, in degrees, that has a negative sine and a positive cosine. (2 points)




Part V: Using your calculator, confirm your choice by writing the cosine of your angle and the sine of your angle below. (4 points)

Answer 75

Oh :O you dont have to

Answer 76

nah i'm just joking i'll get on it :P

Answer 77

Ha

Answer 78

Part I: Triangle ABC is called a special right triangle. What kind of special right triangle is it (2 points)

since the angles are 30, 60 and 90, we call this a "30-60-90 triangle" as its name (so that would be it)

Answer 79

for part II: the sum of the angles in a triangle are 180 as usual so

90 + BCD + 30 = 180, solve for BCD

Answer 80

70

Answer 81

almost, check your calculations again

Answer 82

60

Answer 83

good, 60

Answer 84

Part III: Complete the sentence below.

In a 30-60-90 right triangle, the length of the hypotenuse is ________ times the length of the short leg, and the length of the long leg is _______ times the length of the short leg. (4 points)

this is just something you need to memorize

length of the hypotenuse is twice the length of the short leg

long leg is sqrt(3) times the length of the short leg

Answer 85

twice as long as the shorter leg

Answer 86

for the first blank

Answer 87

good, second would be sqrt(3)

Answer 88

cool

Answer 89

Part IV: Using what you know about these special triangles, calculate the length of side BC. Show your work in words or equations. (4 points)

we can use the answer for part III as a guide - the side BC is the hypotenuse and the short side is 10, so hypotenuse = ?

Answer 90

20

Answer 91

20

Answer 92

20

Answer 93

awesome, 20


Part V: Use your knowledge about the relationship between side lengths of this triangle to find the length of side AC. Show your work in words or equations. (4 points)

so, for AC, we consider only the small triangle on the left as our 30-60-90 triangle

AC is the hypotenuse, and the long leg is 10

so if long leg = short leg *sqrt(3) what's the short leg? (you can leave it in radical form, don't convert it to a decimal)

Answer 94

like this

Answer 95

yes

when you plug it into your calculator it's going to give it in decimal form so let's do it manually

if we divide both sides by sqrt(3)

short side = 10/sqrt(3)

and the hypotenuse is just double the short side, so hypotenuse = 20/sqrt(3)

Answer 96

I know some schools are picky about not having radicals in the denominator so we can re-write this as 20*sqrt(3)/3 = hypotenuse

Answer 97

for part IV we need to treat the entire triangle as one big 30-60-90 triangle so let's put everything we know so far

Answer 98

we can use the pythagorean theorem to find the big hypotenuse at the bottom

20^2 + (20/sqrt(3))^2 = hypotenuse^2 solve for hypotenuse, leave your answer in radical form

Answer 99

40sqrt3/3

Answer 100

awesome, just be careful how you write that, there should be a parentheses around the first 3

40sqrt(3) / 3

Answer 101

Thanks!!