Given that cos A = 5/13 and A and B are both acute angles, calculate the value of Sin2A and Cos2A
since cosA = 5/13, sinA = 12/13
Now just use those values in your double-angle formulas.
sinA=120 and cosA=-144/169
To find the value of sin 2A and cos 2A, we need to use trigonometric identities. One useful identity is:
sin 2A = 2sin A * cos A
cos 2A = cos^2 A - sin^2 A
First, let's find sin A. Since A is an acute angle, we can use the Pythagorean identity sin^2 A + cos^2 A = 1:
sin A = sqrt(1 - cos^2 A)
= sqrt(1 - (5/13)^2)
= sqrt(1 - 25/169)
= sqrt(144/169)
= 12/13
Now we can substitute sin A and cos A into the formulas for sin 2A and cos 2A:
sin 2A = 2sin A * cos A
= 2 * (12/13) * (5/13)
= 120/169
cos 2A = cos^2 A - sin^2 A
= (5/13)^2 - (12/13)^2
= (25/169) - (144/169)
= -119/169
Therefore, sin 2A = 120/169 and cos 2A = -119/169.