Question

If sin Θ = 2 over 3 and tan Θ < 0, what is the value of cos Θ?

square root 5 over 2

negative square root of 5

square root of 5 over 3

negative square root of 5 over 3

Answer 1

@hartnn can you help me with this triq question?

Answer 2

uhh... i can't spell.. >.< its trig, not triq haha

Answer 3

First, figure out the quadrant in which sin is + and tan is -

Answer 4

tan is - in quadrants II and IV
and sin is + in quadrants I and II

Answer 5

ok, since tan(theta) is negative, and sin(theta) is postive, what can you tell about cos(theta)? (Remember that tan = sin/cos).

Answer 6

so it has to be negative, right?

Answer 7

oh, so would i convert the "tan = sin/cos" to solve for cos?

Answer 8

well... you can't really "solve" for cos because you were not given a number for tan. You can however, figure out the position of sin in the unit circle. What are the possible numbers for sin?

Answer 9

ahh, ok uh so
2/3 is sin ...

Answer 10

use,
\(\Large \sin^2 x+\cos^2 x=1\)

Answer 11

what is x?

Answer 12

and you have correctly determined that cos should be negative
because tan = sin / cos
for than to be negative since sin is positive, cos must be negative

Answer 13

x is the angle
here, its theta

Answer 14

\(\sin \theta = 2/3 \\ \cos\theta = \sqrt{1-\sin^2 \theta}=...\)

Answer 15

Please use the Pythagorean theorem to find the value of cos from the given value of sin. For this first draw a triangle

Now by Pythagorean theorem the other side is equal to sqrt(9 - 4) = sqrt(5).

cos(theta) = adjacent / hypotenuse = sqrt(5) / 3.

Can you do it from here?

Answer 16

oh, and thats an alternative method, the triangle to solve the same problem ^^

Answer 17

so which one should I use?

Answer 18

well, look at both, use the one which u find easy.
but its better if you know both....maybe you can use both to verify your answer

Answer 19

i mean use one to find the answer and other to verify it

Answer 20

ok, makes sense... so I'll start with the equation... i guess

Answer 21

sure
tell us what you got for cos

Answer 22

ok, so... is x necessarily equal to something?

Answer 23

x is an angle, like theta
\(\sin^2 \theta +\cos^2 \theta =1\)
better ?
you know sin theta, find cos theta from there,,,

Answer 24

\(\Large (2/3)^2 + \cos^2 \theta =1 \)

Answer 25

uhm, so I tried to solve, and I got
139/250 .... ? it doesn't sound right to me.....

Answer 26

how...

\(\cos^2 \theta = 1- 4/9 = 5/9\)
take square root now

Answer 27

>.< for how: that's what my calculator says... O.o
the square root of 5/9... right?
ok, so I got 0.745 ...

Answer 28

Don't use a calculator for such calculations. Square root of 5/9 is sqrt(5) over sqrt(9), which gives you sqrt(5)/3

Thus cos(theta) = sqrt(5)/3 and that is your answer

Answer 29

no need of calculator, i guess u know, square root of 9 is 3
\(\cos^2 \theta = 5/9 \\ \cos \theta = \sqrt{(5/9)}= \sqrt5 /\sqrt 9 = \sqrt 5/3\)

and don't forget to add a negativee sign

Answer 30

so, actually, cos theta = - sqrt 5/3

Answer 31

oh, ok so i don't have to simplify it to a solid number ?

Answer 32

look at your choices

Answer 33

ohhhhh wait.... no >.<
okay then haha
hartnn: yup, just looked at them.....

Answer 34

ok, ask if any more doubts on this :)

Answer 35

soo, if I use the other method...

Answer 36

did you get how he got that triangle ? the 2 sides on it ?

Answer 37

because getting 3rd side is easy, a pythagoras theorem.

Answer 38

hmm ..... did he get the values of the 2 sides from the 2/3 ?

Answer 39

yes
since sin = opposite side/ hypotenuse = 2/3
he too
opposite side = 2
hypotenuse = 3
makes sense ?
thats what u do always

Answer 40

he took*

Answer 41

OHH!! I Just got it! ok!

Answer 42

yes it make sense, thank you so so much! :D

Answer 43

welcome ^_^

Answer 44

Ahem. Provide a solution or counter example. LOL xD

Answer 45

O.o