Question

Найдите значения cos a и tg a если sin a =5/13​

Answer 1

Ответ:

25/65

Объяснение:

Answer 2

To find the values of cos(a) and tan(a) given that sin(a) = 5/13, we can use the Pythagorean identity and the definitions of cosine and tangent:

1. Pythagorean identity: sin^2(a) + cos^2(a) = 1
2. Definition of tangent: tan(a) = sin(a) / cos(a)

We are given sin(a) = 5/13. Let's use this information to find the values of cos(a) and tan(a).

Step 1: Find cos(a) using the Pythagorean identity.

sin^2(a) + cos^2(a) = 1 (5/13)^2 + cos^2(a) = 1 25/169 + cos^2(a) = 1 cos^2(a) = 1 - 25/169 cos^2(a) = (169 - 25) / 169 cos^2(a) = 144 / 169

cos(a) can be either positive or negative, depending on the quadrant of the angle a. Since sin(a) is positive (5/13), a must be in either the first or second quadrant. In these quadrants, cos(a) is positive. Therefore,

cos(a) = √(144 / 169) = 12/13 (positive value)

Step 2: Find tan(a) using the definition of tangent.

tan(a) = sin(a) / cos(a) tan(a) = (5/13) / (12/13) tan(a) = 5/12

So, the values of cos(a) and tan(a) are:

cos(a) = 12/13 tan(a) = 5/12