Найдите значение cosa,если sina=√2/3 и 0<а<п/2

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Given that sina = √2/3 and 0 < a < π/2, we can use the trigonometric identity sin^2a + cos^2a = 1 to find the value of cos a.

sina = √2/3
Now, we can square both sides to get rid of the square root:

sin^2a = (√2/3)^2
sin^2a = 2/3

Next, we can use the trigonometric identity cos^2a = 1 - sin^2a to find the value of cos a:

cos^2a = 1 - sin^2a
cos^2a = 1 - 2/3
cos^2a = 1/3

Taking the square root of both sides gives us:

cos a = ±√1/3
cos a = ±√1/√3
cos a = ±1/√3

Since a is in the first quadrant (0 < a < π/2), cos a must be positive. Therefore:

cos a = 1/√3

Therefore, the value of cos a when sina = √2/3 and 0 < a < π/2 is 1/√3.