Given:cosA= 4/5 0(less than or equal to)A(less than of equal to)90*
find sinA, sin2A, cos2A
cosA = 4/5 or opposite = 4, hypotenuse = 5
you should recognize the 3-4-5 triangle,
then sinA = 3/5
sin 2A = 2sinAcosA = 2(3/5)(4/5) = 24/25
cos 2A = cos^2 A - sin^2 A
= 16/25 - 9/25 = 7/25
thank you.
To find the value of sinA, we can use the Pythagorean identity:
sin^2 A + cos^2 A = 1
Since we know the value of cosA, we can substitute it into the equation to solve for sinA:
sin^2 A + (4/5)^2 = 1
sin^2 A + 16/25 = 1
sin^2 A = 1 - 16/25
sin^2 A = 9/25
sin A = sqrt(9/25)
sin A = 3/5
Therefore, sinA = 3/5.
To find sin2A, we can use the double angle identity:
sin2A = 2sinAcosA
Substituting the values we already know, we get:
sin2A = 2 * (3/5) * (4/5)
sin2A = 24/25
Therefore, sin2A = 24/25.
To find cos2A, we can use the double angle identity:
cos2A = cos^2 A - sin^2 A
Substituting the values we already know, we get:
cos2A = (4/5)^2 - (3/5)^2
cos2A = 16/25 - 9/25
cos2A = 7/25
Therefore, cos2A = 7/25.