Question

Найдите а) sin a, если cos a=-1/3 б) cos a, если sin a=2/5 в) tg a, если cos a=1/2

Answer 1

решение в приложении

Answer 2

а)

Given: cos(a) = -1/3

We know that sin^2(a) + cos^2(a) = 1 (from the Pythagorean identity). Substituting the given value of cos(a), we get: sin^2(a) + (-1/3)^2 = 1 sin^2(a) + 1/9 = 1 sin^2(a) = 1 - 1/9 sin^2(a) = 8/9 Taking the square root of both sides, we get: sin(a) = √(8/9) sin(a) = (√8)/(√9) sin(a) = (√(4*2))/(3) sin(a) = (2√2)/3

Therefore, sin(a) = (2√2)/3.

б)

Given: sin(a) = 2/5

We know that sin^2(a) + cos^2(a) = 1 (from the Pythagorean identity). Substituting the given value of sin(a), we get: (2/5)^2 + cos^2(a) = 1 4/25 + cos^2(a) = 1 cos^2(a) = 1 - 4/25 cos^2(a) = 25/25 - 4/25 cos^2(a) = 21/25 Taking the square root of both sides, we get: cos(a) = √(21/25) cos(a) = (√21)/(√25) cos(a) = (√(21))/(5)

Therefore, cos(a) = (√(21))/(5).

в)

Given: cos(a) = 1/2

We know that tan(a) = sin(a)/cos(a) (from the definition of tangent). Substituting the given value of cos(a), we get: tan(a) = sin(a)/(1/2) tan(a) = 2sin(a)

Since cos(a) = 1/2, this means that the angle a is in the first quadrant or the fourth quadrant. In the first quadrant, both sine and tangent are positive. Therefore, we can conclude that: tan(a) = 2sin(a) tan(a) = 2(√(1 - cos^2(a))) tan(a) = 2(√(1 - (1/2)^2)) tan(a) = 2(√(1 - 1/4)) tan(a) = 2(√(3/4)) tan(a) = 2(√(3))/(√(4)) tan(a) = 2(√(3))/2 tan(a) = √(3)

Therefore, tan(a) = √(3).