Question

If cos Θ = negative two over five and tan Θ > 0, what is the value of sin Θ?

Answer 1

Use \[
\cos^2\theta+\sin^2\theta = 1
\]

Answer 2

That will give you the absolute value. The part about \(\tan\theta >0\) it just to let you know which quadrants it is in.

Answer 3

???

Answer 4

I know it is not "Square Root of 21 over 5"

Answer 5

there is a picture of an angle with cosine \(\frac{2}{5}\)
you are missing the sine, which you do by finding the missing side via pythagoras

Answer 6

It is -2/5

Answer 7

The Cosine

Answer 8

@satellite73

Answer 9

@satellite73???

Answer 10

Hello?

Answer 11

did you find the length of the missing side?

Answer 12

No, the cosine is -2/5

Answer 13

You gave me an angle for 2/5

Answer 14

fine
you still need the length of the missing side
i am not interested in whether it is positive or negative at the moment because i cannot draw a triangle with one side negative length
we can worry about the sign of the answer later

Answer 15

then the sin should equal The Square Root Of 29, negative or not.

Answer 16

no

Answer 17

Correct?

Answer 18

not even close

Answer 19

Oh

Answer 20

use pythagoras to find the missing side
it is not \(\sqrt{29}\) for sure

Answer 21

hint, it is a side, not the hypotenuse

Answer 22

ohhh!

Answer 23

what do you get for the side?

Answer 24

the square root of 21

Answer 25

right
and that is not the sine, that is just the length of the side
the sine is the opposite over the hypotenuse

Answer 26

yes

Answer 27

that makes your answer
\[-\frac{\sqrt{21}}{5}\]

Answer 28

i will let you figure out why it has to be negative

Answer 29

Thank you so much!

Answer 30

yw