Question

Найти sin2a, sina=5/13

Answer 1

Ответ:

± 120/169.

Пошаговое объяснение:

sin2a = 2•sina•cosa.

1) sin²a + cos²a = 1, тогда

lcosal = √(1-sin²a) = √(1 - 25/169) = 12/13.

2) Если cosa > 0, то sin2a = 2•5/13•12/13 = 120/169.

Если cosa < 0, то sin2a = 2•5/13•(-12/13) = - 120/169.

Answer 2

To find sin(2a) given that sin(a) = 5/13, we can use the double-angle identity for sine:

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

However, to use this identity, we also need to find the value of cos(a). We can use the Pythagorean identity for sine and cosine:

sin^2(a) + cos^2(a) = 1

Given that sin(a) = 5/13, we can find cos(a):

sin^2(a) + cos^2(a) = 1 (5/13)^2 + cos^2(a) = 1 25/169 + cos^2(a) = 1 cos^2(a) = 1 - 25/169 cos^2(a) = 144/169 cos(a) = ± √(144/169)

Since sin(a) is positive (5/13), we take the positive square root:

cos(a) = √(144/169) = 12/13

Now, we can find sin(2a):

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

So, sin(2a) = 120/169.