In triangle ABC, the angle is 90 degrees, sinA = 3 √ 11 divided by 10. Find cosA.

According to the basic trigonometric identity

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

cos A = (1 – (sin A) ^ 2) ^ 0.5.

Thus, if sin A = 3 * 11 ^ 0.5 / 10, then

cos A = (1 – (3 * 11 ^ 0.5 / 10) ^ 2) ^ 0.5 = (1 – 99/100) ^ 0.5 = (1/100) ^ 0.5 = 1/10 …

The positive value of the radical expression is taken, since the degree measure of the angle lies in the range from 0 ° to 90 ° and, accordingly, the value of cos A lies in the range from 0 to 1.