Question

Найти tg2a если sina=-40/41

Answer 1

Решение
2) sina=40/41
cosa=sqrt(1-sin^2(a))=sqrt(1-1600/1681)=9/41
tga=sina/cosa=(40/41)/(9/41)=40/9
ctga=1/tga=9/40
3) sina=0,5
cosa=sqrt(1-sin^2(a))=sqrt(1-0,25)=0,5√3
tga=sina/cosa=0,5/(0,5√3)=√3/3
ctga=1/tga=√3

Answer 2

To find the value of tg(2a) given sin(a) = -40/41, we can use the trigonometric identity:

tg(2a) = 2 * sin(a) / (1 - sin^2(a))

First, let's calculate sin^2(a):

sin^2(a) = (-40/41)^2 = 1600/1681

Now, substitute the values into the identity:

tg(2a) = 2 * (-40/41) / (1 - 1600/1681) = (-80/41) / (81/1681) = (-80/41) * (1681/81) = -80 * 1681 / (41 * 81)

Evaluating this expression:

tg(2a) ≈ -3360 / 3321

Therefore, tg(2a) is approximately -3360/3321.