Question

Найдите sin2a если sin= 5/13 , 90*

Answer 1

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Answer 2

To find the value of sin(2a), we can use the double-angle formula for sine:

sin(2a) = 2 * sin(a) * cos(a)

Given that sin(a) = 5/13 and a = 90 degrees, we need to find cos(a) first.

Using the Pythagorean trigonometric identity: sin^2(a) + cos^2(a) = 1

sin^2(a) = (5/13)^2 = 25/169

cos^2(a) = 1 - sin^2(a) = 1 - 25/169 = (169 - 25)/169 = 144/169

cos(a) = √(144/169) = 12/13 (cosine is positive in the second quadrant where 90 degrees lies)

Now, we can calculate sin(2a):

sin(2a) = 2 * sin(a) * cos(a) sin(2 * 90 degrees) = 2 * (5/13) * (12/13) sin(180 degrees) = 2 * 5 * 12 / (13 * 13) sin(180 degrees) = 120 / 169

So, sin(2a) is equal to 120/169.