If sinA=0.5 , what is the value of cos2A and sin2A?
You do not even need the trig formulas for this because if sin A = .5 then in the first quadrant A = 30 degrees
so 2A = 60 degrees
cos 60 = 1/2
sin 60 = (1/2)sqrt 3
To find the value of cos2A and sin2A, we can use the identities:
cos2A = cos^2(A) - sin^2(A)
sin2A = 2 * sin(A) * cos(A)
Given that sinA = 0.5, we can substitute this value into the identities.
cos2A = cos^2(A) - sin^2(A)
cos2A = cos^2(A) - (0.5)^2
cos2A = cos^2(A) - 0.25
sin2A = 2 * sin(A) * cos(A)
sin2A = 2 * 0.5 * cos(A)
sin2A = 1 * cos(A)
sin2A = cos(A)
Therefore, the value of cos2A is cos^2(A) - 0.25, and the value of sin2A is equal to cos(A).
To find the value of cos2A and sin2A when sinA=0.5, we can use trigonometric identities.
The identity that relates cos2A and sin2A is:
sin^2A + cos^2A = 1
We can rewrite this equation as:
cos^2A = 1 - sin^2A
Now, substitute sinA=0.5 into the equation:
cos^2A = 1 - (0.5)^2 = 1 - 0.25 = 0.75
Taking the square root of both sides, we can find the value of cosA:
cosA = ± √0.75
cosA can have positive or negative values, which depend on the quadrant in which angle A is located. However, we are only interested in finding cos2A and sin2A, so we will continue using the positive square root.
Now, let's find sin2A using the double-angle identity for sine:
sin2A = 2sinAcosA
Substituting sinA=0.5 and cosA=√0.75, we have:
sin2A = 2(0.5)(√0.75) = √0.75
Therefore, the value of cos2A is √0.75 and sin2A is also √0.75.