Question

Найдите Sin A и Tg A, если Cos A = 2/7

Answer 1

Cos A = 2/7           0 < A < π/2 (I четверть)
sin^2 A = 1 - cos^2 A = 1 - (2/7)^2 = 1 - 4/49 = 45/49 => cos √45/√49 = 3√5/7
tg A = sin A/cos A  = 3√5 · 2 / 7 · 7 = 6√5/49

Answer 2

To find Sin A and Tan A when Cos A = 2/7, we can use the Pythagorean trigonometric identity:

Sin^2 A + Cos^2 A = 1

Since we know Cos A = 2/7, we can solve for Sin A:

Sin^2 A + (2/7)^2 = 1 Sin^2 A + 4/49 = 1 Sin^2 A = 1 - 4/49 Sin^2 A = 45/49

Now, taking the square root of both sides to find Sin A:

Sin A = ±√(45/49)

Since Sin A represents the y-coordinate of the point on the unit circle and is positive in the first and second quadrants, we take the positive square root:

Sin A = √(45/49) = √45 / 7

Now, to find Tan A, we can use the identity:

Tan A = Sin A / Cos A

Tan A = (√45 / 7) / (2/7) Tan A = √45 / 2

So, the values are: Sin A = √45 / 7 Tan A = √45 / 2