Question

Найти cosx, tgx, ctgx, если: sinx=1/2, 0

Answer 1

Решение задания смотри на фотографии

Answer 2

To find the values of cos(x), tan(x), and cot(x) given that sin(x) = 1/2 and 0 < x < π, we can use trigonometric identities. Since sin(x) = 1/2, we can use the Pythagorean identity to find cos(x), and then calculate tan(x) and cot(x) accordingly.

Here's how you can do it step by step:

Step 1: Find cos(x) Using the Pythagorean identity: sin^2(x) + cos^2(x) = 1 Substitute sin(x) = 1/2 into the equation: (1/2)^2 + cos^2(x) = 1 1/4 + cos^2(x) = 1 cos^2(x) = 1 - 1/4 cos^2(x) = 3/4

Since 0 < x < π, we know that cos(x) is positive, so we take the positive square root: cos(x) = √(3/4) = √3/2

Step 2: Find tan(x) Using the definition of tangent: tan(x) = sin(x) / cos(x) Substitute sin(x) = 1/2 and cos(x) = √3/2 into the equation: tan(x) = (1/2) / (√3/2) tan(x) = 1 / √3

Step 3: Find cot(x) Using the definition of cotangent: cot(x) = 1 / tan(x) Substitute tan(x) = 1 / √3 into the equation: cot(x) = 1 / (1 / √3) cot(x) = √3

So, the values of the trigonometric functions are: cos(x) = √3/2 tan(x) = 1 / √3 cot(x) = √3