Question

If sin θ = 1/3 and tan θ < 0, what is the value of cos θ?

Answer 1

draw a triangle

Answer 2

there is a picture of an angle whose sine is \(\frac{1}{3}\)
find the missing side via pythagoras

Answer 3

you can pretty much do it in your head
what is \(3^2\)?

Answer 4

9

Answer 5

and \(1^2\)?

Answer 6

1

Answer 7

and \(9-1\)?

Answer 8

8

Answer 9

so answer for the missing side is \(\sqrt{8}\)
now two more steps

Answer 10

2√2

Answer 11

yeah that too
now the cosine is adjacent over hypotenuse, but don't forget that \(\tan(\theta)<0\) which means the cosine must be negative

Answer 12

-√8/3

Answer 13

or -(2√2)/3

Answer 14

yes
probably your teacher will like the second one more

Answer 15

YES! thank you! you're gr8 :)

Answer 16

lol yw