Question

Найдите cos A,если: а)tg A=3

Answer 1

тгА=корень3, т.е тг=60

кос60=1\2

Answer 2

To find the value of cos A when tan A = 3, we can use the relationship between the trigonometric functions. The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side.

We know that: tan A = opposite side / adjacent side

Let's assume that the opposite side is represented by "y" and the adjacent side is represented by "x". So, we have:

tan A = y / x = 3

Now, we can use the Pythagorean identity for right triangles: sin^2 A + cos^2 A = 1

Since we know that tan A = 3, we can find the value of sin A using the Pythagorean identity: sin^2 A = 1 / (1 + tan^2 A) = 1 / (1 + 3^2) = 1 / 10

Now, we can find sin A: sin A = sqrt(1 / 10) = sqrt(10) / 10

Finally, we can find cos A using the relationship between sine and cosine: cos A = sqrt(1 - sin^2 A) = sqrt(1 - 10/100) = sqrt(90/100) = sqrt(9/10) = 3/√10

So, the value of cos A when tan A = 3 is 3/√10.