If sin(A)=square root of 5/3 with A in quad 1, evalutate cos (2A)?

Question

Please be very detailed

Answer 1

I'm assuming you mean sin(A) = sqrt(5)/3, because sqrt(5/3) >1, which is impossible for real values of A.

By a fundamental trigonometric identity, cos(2A) = (cos(A))^2 - (sin(A))^2 (1).

since (cos(A))^2 + (sin(A))^2 = 1, it follows (cos(A))^2 = 1 - ((sqrt(5)/3)^2 = 1 - 5/9 = 4/9.

Pugging the values in identity (1), we get

cos(2A) = 4/9 - 5/9 = -1/9.

Here, it doesn't matter that A is in the first quadrant.

Answer 2

this is impossible because the square root of 5/3 is greater than 1, and sin of anything can never be greater than 1, so this makes no sense

Answer 3

This question doesn't make sense, since the sin of any angle must be a positive number between 0 and 1