Question

Given that sinθ=35 , what is cosθ?

Answer 1

@princeevee do you know the relationship between sin theta and cosine theta?

Answer 2

not really, i kinda forget stuff, can you refresh me on it?

Answer 3

Suppose theta represents an angle of a right triangle:

Answer 4

Then \(\sin(\theta) = \dfrac{a}{c}\) and \(\cos(\theta) = \dfrac{b}{c}\)
\(a = c\sin(\theta)\) and \(b = c\cos(\theta)\)

And then you use pythagorean theorem at this point:
\(a^2 + b^2 = c^2\)

Which means:
\((c\sin(\theta))^2 + (c\cos(\theta))^2= c^2\)

which simplifies to:
\(c^2\sin^2(\theta) + c^2(\cos^2(\theta) = c^2\)

Factor out the \(c^2\) on the LHS to get:
\(c^2(\sin^2(\theta) + \cos^2(\theta)) = c^2\)
Divide both sides by \(c^2\) to get

\(\sin^2(\theta) + \cos^2(\theta) = \dfrac{c^2}{c^2}\)
or simply:


\(\sin^2(\theta) + \cos^2(\theta) = 1\)

Answer 5

We know \(\sin(\theta) = 35\) so we insert that in to the formula to get:

\(35^2 + \cos^2(\theta) = 1\)

The continue solving for \(\cos(\theta)\)

BTW, \(\cos^2(\theta)\) and \((\cos(\theta))^2\) mean the same thing\

Answer 6

Any questions @princeevee ?

Answer 7

i'm still a bit confused..

Answer 8

About what?

Answer 9

the final answer is a fraction, right?

Answer 10

so do i need to have a number to place the cosine theta to complete the equation?

Answer 11

We have to isolate \(\cos(\theta)\) in the equation \(35^2+ \cos^2(\theta) = 1\)

Answer 12

What must we do first in order to accomplish this?

Answer 13

i...dont remember..

Answer 14

Subtract 35^2 from both sides. What do you get?

Answer 15

so 35^2 - 35^2 and cos(theta) - 35^2?

Answer 16

It's \(\sin(\theta) = 35\) not \(\theta= 35\)

Answer 17

nvm, I read that wrong sorry to confuse you.

Answer 18

Yea I noticed ty srry to interrupt

Answer 19

is my way of subtracting right?

Answer 20

Do you know how to subtract a number from both sides?

Answer 21

that's -1224, right?

Answer 22

Correct and remember what I said earlier. You can't take the square root of a negative number.

Answer 23

So what does this mean in terms of cosine theta?

Answer 24

the theta is positive?

Answer 25

if \(\cos^2(\theta) = -1224\) what is the next step?

Answer 26

i dont know then..

Answer 27

Have you even taken the square root of both sides?

Answer 28

of an equation?

Answer 29

i did, it's just this is all confusing..

Answer 30

@Hero ?

Answer 31

Sorry to hear that.

Answer 32

The point is, you can't take the square root of a negative number and expect a real number result.

Answer 33

so what do we do to make it a positive?

Answer 34

If a number is negative, then it is negative. You can't make a negative number positive.

Answer 35

so something went wrong with the subtraction?

Answer 36

if you look, \(\cos(\theta) = b/c\) what is \(b/c\) ?

Answer 37

opposite / hypotenuse?

Answer 38

wait, i wrote something wrong!

Answer 39

it's 3/5, not 35

Answer 40

smh

Answer 41

i know, sorry..

Answer 42

This is why I don't help users with questions. I end up wasting my own time.

Answer 43

....

Answer 44

You might as well just post a new question.

Answer 45

so i just post the same one with the correct changes?

Answer 46

exactly