Question

Если cosα=9/41, то sinα=

Answer 1

sinα = +√(1 – cos2α) = √(1 – (9/41)2) = 40/41

Answer 2

To find the value of sinα given that cosα is equal to 9/41, we can use the Pythagorean identity for trigonometric functions:

sin^2α + cos^2α = 1

Rearranging this equation, we have:

sin^2α = 1 - cos^2α

Since we know that cosα is 9/41, we can substitute this value into the equation:

sin^2α = 1 - (9/41)^2

Now we can solve for sinα by taking the square root of both sides:

sinα = ±√(1 - (9/41)^2)

Evaluating this expression, we get:

sinα ≈ ±√(1 - 81/1681)

sinα ≈ ±√(1600/1681)

sinα ≈ ±(40/41)

Therefore, sinα can be either +40/41 or -40/41, depending on the quadrant in which α lies.