# Thread: find cos (A) and tan (A)

1. ## find cos (A) and tan (A)

hi all,
i have problem with this subject..
Given that sin (A)=-1/2, find the value of find cos (A) and tan (A)??

thanks...

2. Originally Posted by pencil09
hi all,
i have problem with this subject..
Given that sin (A)=-1/2, find the value of find cos (A) and tan (A)??

thanks...
I assume you're familiar with the following basic formulas of trigonometry:
cos²x + sin²x = 1
tan x = sin x / cos x

So, if you know that sin (A) = -1/2, you get
cos²A + (-1/2)² = 1 <=> cos²A = 1 - 1/4 <=> cos²A = 3/4
cos A = ± sqrt(3)/2
Whether cos A is positive or negative depends on the quadrant that the angle A is in.

Once you know that sin A = -1/2 and cos A = ± sqrt(3)/2 , you can calculate tan A by applying the second formula:
tan A = (-1/2)/(± sqrt(3)/2) so tan A = ±(1/sqrt(3)) , again depending on the quadrant.

This is my first post on these forums, but I hope I was able to help.

I assume you're familiar with the following basic formulas of trigonometry:
cos²x + sin²x = 1
tan x = sin x / cos x

So, if you know that sin (A) = -1/2, you get
cos²A + (-1/2)² = 1 <=> cos²A = 1 - 1/4 <=> cos²A = 3/4
cos A = ± sqrt(3)/2
Whether cos A is positive or negative depends on the quadrant that the angle A is in.

Once you know that sin A = -1/2 and cos A = ± sqrt(3)/2 , you can calculate tan A by applying the second formula:
tan A = (-1/2)/(± sqrt(3)/2) so tan A = ±(1/sqrt(3)) , again depending on the quadrant.

This is my first post on these forums, but I hope I was able to help.

which mean there are more than 1 answer in this case....
The two quadrant that involve are Q-3 and Q-4, because in that quadrant the value for sin A is negative, is it true??

so the answer can like this,
cos A = - sqrt(3)/2 and tan A= (1/sqrt(3))
in Q-4,
cos A = sqrt(3)/2 and tan A= -(1/sqrt(3))

is it true???

4. Originally Posted by pencil09

so the answer can like this,