Question

CosA 5/17. Найти sin A, tg A, Ctg A

Answer 1

cos² a+ sin²a=1

25/289+sin² a =1

sin a = √264 /17=2√66/17

tg a= sin a/cos a=2√66/5

ctg a=5/2√66 = 5√66/132

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Answer 2

To find sin A, tg A, and Ctg A, we can use the given information that CosA = 5/17. We'll use the Pythagorean identity to find sin A and then use the definitions of tangent and cotangent to find tg A and Ctg A, respectively.

1. Pythagorean Identity: sin^2 A + cos^2 A = 1
2. Definition of Tangent: tg A = sin A / cos A
3. Definition of Cotangent: Ctg A = cos A / sin A

Step 1: Find sin A using the Pythagorean identity: sin^2 A + cos^2 A = 1 sin^2 A + (5/17)^2 = 1 sin^2 A + 25/289 = 1 sin^2 A = 1 - 25/289 sin^2 A = (289 - 25) / 289 sin^2 A = 264 / 289

Now, take the square root of both sides to find sin A: sin A = √(264 / 289) sin A ≈ √(264) / √(289) sin A ≈ ±16.248 / 17 (Note: sin A can be positive or negative in different quadrants.)

Step 2: Find tg A using the definition of tangent: tg A = sin A / cos A tg A ≈ (±16.248 / 17) / (5/17) tg A ≈ ±16.248 / 5 (Note: tg A can be positive or negative in different quadrants.)

Step 3: Find Ctg A using the definition of cotangent: Ctg A = cos A / sin A Ctg A ≈ (5/17) / (±16.248 / 17) Ctg A ≈ 5 / (±16.248) (Note: Ctg A can be positive or negative in different quadrants.)

It's important to determine the sign of sin A, tg A, and Ctg A based on the quadrant in which angle A lies. Since the information about the quadrant of angle A is not provided, the signs of these trigonometric functions remain undetermined.