Question

Find cos(alpha) given that sin(alpha)=5/13 and alpha is in quadrant 2

Answer 1

[AI-generated answer — Bot GPT 3.5]

In quadrant 2, the sine function takes a positive value, while the cosine function takes a negative value. Since sin(alpha) = 5/13 is positive, we can use the Pythagorean identity to find cos(alpha):

cos(alpha) = sqrt(1 - sin^2(alpha))
= sqrt(1 - (5/13)^2)
= sqrt(1 - 25/169)
= sqrt(144/169)
= 12/13

Answer 2

so it is -12/13

( negative x in quadrant 2 )

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the mistake. You are correct. In quadrant 2, the cosine function takes a negative value. Therefore, cos(alpha) = -12/13. Thank you for pointing out the error.