Question

Find cos theta if sin theta = -12/13 and tan theta > 0

Answer 1

@ganeshie8

Answer 2

Hello, how would I solve this? Should I be drawing a triangle?

Answer 3

why is 13 on the long side? Is it not the top of the fraction going to the longer side?

Answer 4

missed the negative?

Answer 5

you need to recognise this this is a 3rd quadrant angle and a iwll be negative... and 12 should be shown as a -12

Answer 6

sine is opposite over hypotenuse
forget the negative, find the length of the other side
you can decide if your answer is positive or negative once you get the length of the other leg

Answer 7

wait, sin = opposite over hypothesis so that is why 13 is on the long side, correct?

Answer 8

yes

Answer 9

"long side" you mean "hypotenuse" right?

Answer 10

i would use Pythagorean right? so

Answer 11

And that only applies to right angle triangle.

Answer 12

\[\sqrt{13}^2 - \sqrt{12}^2\]

Answer 13

yes or recall this very famous right triangle
not as famous as 3- 4 - 5 but almost

Answer 14

no
\[\sqrt{13^2-12^2}\]

Answer 15

yes, i tried to write that but i didn't know how, sorry

Answer 16

\[a^2+12^2=13^2\\
a^2=13^2-12^2\\
a=\sqrt{13^2-12^2}\]

Answer 17

you will see this nice triangle again and again
almost as often as you see \(3:4:5\) and it relatives \(6:8:10\) etc

Answer 18

a = 5

Answer 19

cos = 5/13?

Answer 20

but it is negative right? why?

Answer 21

no be careful
yes it is negative

Answer 22

it is negative because you are told that tangent is positive, and tangent is sine over cosine, so if tangent is positive and sine is negative, then cosine must be negative too

Answer 23

really? that makes sense, thank you very much, i think i understand how to do this now, for any problem i would repeat similar steps

Answer 24

or if you like to think of it this way, if sine is negative and tangent is positive, you must be in quadrant 3
it is the same thing really
you are welcome

Answer 25

i have one quick question

Answer 26

can you answer it quickly?

Answer 27

if i know it

Answer 28

for a problem like \[\frac{ \tan \Theta }{ \sec \Theta } \]

Answer 29

i would need to know the fundamentals right? or would i be able to solve it without it?

Answer 30

to simplify it is usually algebra

Answer 31

you need to know how to write each of these in terms of sine and cosine, most of the problems require little or no trig, only algebra

Answer 32

for example you have
\[\huge\frac{\frac{\sin(x)}{\cos(x)}}{\frac{1}{\cos(x)}}\]

Answer 33

sin(x)/1

Answer 34

the cosines cancel and you get sin(x)

Answer 35

but how do you know sec = 1/cos(x)

Answer 36

if you write sin(x)/1 your teacher will think you are kind of dumb, so don't do it

Answer 37

haha you're right

Answer 38

it is the definition of secand

Answer 39

secant

Answer 40

that is why you do not have a secant button on your calculator, it is not necessary
it is the reciprocal of cosine

Answer 41

So if i googled the definitions of sec, sine, cos, and more i could solve these questions?

Answer 42

there are a whole lost of trig ratios and identities you can find on gogle.

Answer 43

Google*

Answer 44

you need to memorize them

Answer 45

okay, thank you very much again

Answer 46

you are welcome again
good luck with your trig class

Answer 47

wow wow wow! Thank you for the sheet!!!

Answer 48

make sure to look at the unit circle on the last page

Answer 49

that gives you the values for sine and cosine for lots of angles, both in degrees and in radians

Answer 50

Thank you very very much! Merry almost Christmas and happy Hanuka!

Answer 51

merry christmas to you too
or whatever

Answer 52

lol