Question

Найдите cos Альфа и tg альфа, если sin альфа = 0,8, где альфа - острый угол.

Answer 1

Sin² a + cos² a=1(3/8)² + cos² a=1cos² a=1 - 9/64cos² a = 55/64cos a = √55/8tg a = sin a/cos atg a = (3/8) / (√55/8)tg a = (3/8) * (8/√55) = 3/√55

Answer 2

Finding cos Alpha and tg Alpha given sin Alpha = 0.8

To find cos Alpha and tg Alpha given sin Alpha = 0.8, we can use the relationship between sine, cosine, and tangent in a right-angled triangle.

Using the Pythagorean identity sin^2(Alpha) + cos^2(Alpha) = 1, we can find cos Alpha and tg Alpha.

First, let's find cos Alpha: Using the given sin Alpha = 0.8, we can calculate cos Alpha using the Pythagorean identity: cos^2(Alpha) = 1 - sin^2(Alpha) cos^2(Alpha) = 1 - 0.8^2 cos^2(Alpha) = 1 - 0.64 cos^2(Alpha) = 0.36 cos(Alpha) = ±√0.36 cos(Alpha) = ±0.6

Now, let's find tg Alpha: Using the relationship between sine, cosine, and tangent: tg(Alpha) = sin(Alpha) / cos(Alpha) tg(Alpha) = 0.8 / 0.6 tg(Alpha) = 4 / 3

Therefore, cos(Alpha) = ±0.6 and tg(Alpha) = 4 / 3.

These calculations are based on the Pythagorean identity and the relationship between sine, cosine, and tangent in a right-angled triangle