Question

Can one person explain to me on how to find the answers? Not just give them, please. Thanks!

They are all t/f

sin(-136°) = -sin44°

tan(-212°) = tan32°

sec(-45°) = sec45°

cot(-315°) = -cot45°

Thanks so much, y'all!

Answer 1

Hints :

\[\sin(-x) = -sinx\]

\[\cos(-x) = cosx\]

\[\tan(-x) = -tanx\]

Answer 2

So it's basically just rules I have to memorize? Because my lesson was like subtract from 180, take the square root & multiple by 43. Not really, but it was some long, ridiculous process to find the answer. & It was crazy hard.

Answer 3

\[Sec(-x)=secx\]

\[\cot(-x)=-cotx\]

Answer 4

sin(-136°) =

- sin136 = -sin (180 - 44) = -sin44

Answer 5

So..1st one is True...Do..Apply Same For All others Keep in mind abt the quadrant in which they Lie

Answer 6

So I do have to do that thing they taught me? Do I always just subtract from 180? Because there were times they wanted me to take 180 from the angle. Does that make sense?

Answer 7

& wouldn't that make tan(-212°) = tan32° false since it isn't -tan32°?

Answer 8

that is correct, its false.
for such problems, u need to know your trigonometric ratios, and its periodicity
after how many degrees, value sin repeats itself?
and for cos? tan ?

Answer 9

What do you mean repeat itself? Like start the circle over again?

Answer 10

yeah, like sin 90 = 1 and sin (90+360) is also 1
cos 90 = 0 , cos (90+360) is also 0
so yes, drawing a circle would help

Answer 11

tan(-212°)
= - tan(212) = -tan (180 +32) = -tan32

Answer 12

http://assets.openstudy.com/updates/attachments/50113794e4b009397c68ec2f-parthkohli-1343305757650-unitcircle.gif

Answer 13

I have all the values of quadrantal angles if that's what your saying. Like which ones equal 1, 0, -1, and are undefined.

Answer 14

And when determining which quadrant they are in, I take the number given to me, right? So like -80 would be in the fourth quadrant.

Answer 15

yes, -80 is in 4th quad.
and in 4th quad, which ratios are negative ?

Answer 16

sin, tan, csc, cot. (cos & sec are positive)

Answer 17

thats correct.
u should know that tan values repeat itself after every 180 degrees,
and for sin and cos its 360 degrees, then you can make formulas on your own!

Answer 18

I thought they all repeated every 360 degrees..?

Answer 19

sure! tan repeats after 180 means it will repeat after 360 also , right ?
and whatever are the properties of sin , cos , tan., it will be same for cosec, sec, cot respectively, so lets talk about sin,cos and tan only

Answer 20

Okay, I'll try and follow. but I am a tad confused.. Haha (& thanks for helping!)

Answer 21

do u want to develop the formula by yourself ?
like since tan repeats after 180 , tan (180+x) = tan x
tan (x-180) = tan x
tan (180-x) = - tan x [because tan -x= -tan x]

Answer 22

Hm. I would, but I don't know what to do.. & for some reason, those formulas don't make a whole lot of sense to me. I understand how when x & 180 are swapped that it makes your outcome negative. But I don't know how you go to the formula..