Question

Знайти решту тригонометричних функцій, якщо: sin a =8/17, П/2 Срочно"!

Answer 1

Ответ:

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Answer 2

Finding the Remaining Trigonometric Functions

To find the remaining trigonometric functions given that sin(a) = 8/17 and a is in the first quadrant, we can use the Pythagorean identity and the definitions of the trigonometric functions.

1. Finding cos(a): - We know that sin(a) = 8/17. Using the Pythagorean identity, we can find cos(a). - The Pythagorean identity states that sin^2(a) + cos^2(a) = 1. - Therefore, cos^2(a) = 1 - sin^2(a). - Substituting the value of sin(a), we get cos^2(a) = 1 - (8/17)^2. - Solving for cos(a), we get cos(a) = 15/17.

2. Finding tan(a): - We can find tan(a) using the definition of the tangent function. - tan(a) = sin(a) / cos(a). - Substituting the given values, we get tan(a) = (8/17) / (15/17) = 8/15.

3. Finding cot(a), sec(a), and csc(a): - We can find cot(a), sec(a), and csc(a) using the reciprocal relationships between the trigonometric functions. - cot(a) = 1 / tan(a) = 15/8. - sec(a) = 1 / cos(a) = 17/15. - csc(a) = 1 / sin(a) = 17/8.

Therefore, the remaining trigonometric functions for the given sin(a) = 8/17 in the first quadrant are: - cos(a) = 15/17 - tan(a) = 8/15 - cot(a) = 15/8 - sec(a) = 17/15 - csc(a) = 17/8