Question

Cos α, sin 2α, если sinα= 9 13 и π /2 <α<π

Answer 1

Решение в прикреплённом файле

Answer 2

Given that sin α = 9/13 and π/2 < α < π, we can use the Pythagorean identity to find cos α.

Using the Pythagorean identity sin^2 α + cos^2 α = 1, we can substitute sin α = 9/13:

(9/13)^2 + cos^2 α = 1 81/169 + cos^2 α = 1 cos^2 α = 1 - 81/169 cos^2 α = 88/169 cos α = ±√(88/169)

Since α is in the second quadrant (π/2 < α < π), the cosine function is negative. Therefore, cos α = -√(88/169) = -8/13.

Now, let's find sin 2α using the double angle formula for sine:

sin 2α = 2sin α cos α

Substituting the values we found:

sin 2α = 2 * (9/13) * (-8/13) sin 2α = -144/169