Question

Use the given value and the trigonometric identities to find the remaining trigonometric functions of the angle.

cos θ = − 5/9, sin θ > 0

Answer 1

Okay, let's make that drawing again, though following @hartnn 's advice, I'll do it properly this time ;)
DRAW!!!

Answer 2

Cosine is adj/hyp, right?

Answer 3

yes

Answer 4

So, we have cosθ = -(5/9)
We place the 5 and the 9, accordingly...

(Stop me when you don't understand)

Answer 5

i understand

Answer 6

Now, what's the length of this missing side...
(Hint: Pythagorean theorem)

Answer 7

\[\sqrt{106}\] right?

Answer 8

Remember, 9 is your hypotenuse
When you have
a^2 + b^2 = c^2
9 is your c :)

Answer 9

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

Answer 10

\[\sin^2(\theta) = 1-\cos^2(\theta)\]

Answer 11

\[\sqrt{56}\]

Answer 12

\[\sin^2(\theta)=(\frac{- 5 }{ 9 })^2 -1\]

Answer 13

i prefer the method provided by @PeterPan, because it shows you the inside out

Answer 14

So, we can put sqrt(56) on here...
And you can easily get the other trig functions. Be careful though...

Answer 15

@mathsmind
You do need to do this to illustrate the pythagorean identities you posted. Though if you're not allowed to draw, better know the pythagorean (and other) identities by heart!!!
:D

Answer 16

yes that is what i said

Answer 17

i said i prefer the other method to know the inside out

Answer 18

we are allowed to draw on the test

Answer 19

@savac
REMEMBER THIS

Answer 20

although the identity was proven using pyth.

Answer 21

whats that?

Answer 22

ACTS!!!!

Answer 23

ohhhh thats smart

Answer 24

savac PeterPan is doing a great job

Answer 25

@mathsmind
Thanks for the kudos!
Much appreciated :)

Answer 26

So back to this...

Can you now determine the rest of the trig functions of this theta?