Question

HELP ASAP PLEASE - If tanθ = k (where k is negative) find the possible values of sinθ and cosθ. THANKS! :)

Answer 1

not really enough information
one has to be positive, one has to be negative
if \(\sin(\theta)=a\) then \(\cos(\theta)=\frac{a}{k}\) but really there is not a lot to go by here

Answer 2

@satellite73 I know, the question's very broad and brie - that's why I was so confused haha. Thanks anyway :P

Answer 3

brief*

Answer 4

Use the trig identity:
a) 1 + tan^2 a = 1/cos^2x
1 + k^2 = 1/cos^2 x -> cos^2 x = 1/(1 + k^2) -> cos x = Sqr(1/(1 + k^2). Since tan a = k is negative, only the negative answer is accepted.
b) Use the trig identity
1 + cot^2 a = 1/sin^2 a
1 + 1/k^2 = 1/sin^2 a -> sin^2 a = k^2/(k^2 + 1) ->
-> sin a = + or -Sqr(k^2)/(1 + k^2). Since tan a k is negative, both positive and negative answers might be accepted.