Question

Найти cos a и tg a, если sin a =1/4​

Answer 1

Угол с таким синусом может находиться как в первой, так и во второй четверти. Рассматриваем два варианта.

Answer 2

To find the values of cos(a) and tan(a) when sin(a) = 1/4, we can use the Pythagorean identity and the definition of tangent. Here's how:

Given sin(a) = 1/4, we can find cos(a) using the Pythagorean identity: sin^2(a) + cos^2(a) = 1

Substitute sin(a) with its value: (1/4)^2 + cos^2(a) = 1 1/16 + cos^2(a) = 1

Now, solve for cos(a): cos^2(a) = 1 - 1/16 cos^2(a) = 16/16 - 1/16 cos^2(a) = 15/16

Taking the square root of both sides (remembering that cos(a) is positive in the first quadrant): cos(a) = √(15/16)

cos(a) = √15 / 4

Now, to find tan(a), we use the definition of tangent: tan(a) = sin(a) / cos(a)

Substitute sin(a) and cos(a) with their values: tan(a) = (1/4) / (√15 / 4)

Now, to divide by a fraction, we multiply by its reciprocal: tan(a) = (1/4) * (4 / √15)

The 4 in the numerator and denominator cancel out: tan(a) = 1 / √15

To rationalize the denominator, multiply both the numerator and denominator by √15: tan(a) = (√15) / 15

So, the values of cos(a) and tan(a) are: cos(a) = √15 / 4 tan(a) = (√15) / 15