Question

Найдите cosa и tga, если: а) sina=√3/2. б) sina=0.25​

Answer 1

Объяснение:

ищем по треугольнику

а) против. катет = √3

гипотенуза = 2

(определение синуса)

прилежащий катет = 1 (по теореме Пифагора)

cosa=½

tga=√3

б) sin=1/4

прот.к=1

гип.=4

прил.к=√15

ctga=√15/4

tga=1/√15

Answer 2

To find the values of cos(a) and tan(a) given sin(a), we can use the trigonometric identity:

sin^2(a) + cos^2(a) = 1

And the identity for tangent:

tan(a) = sin(a) / cos(a)

Let's solve for each case:

а) Given sin(a) = √3/2

1. Find cos(a): Using the identity sin^2(a) + cos^2(a) = 1, we can rearrange it to solve for cos(a):

cos^2(a) = 1 - sin^2(a)

cos^2(a) = 1 - (√3/2)^2

cos^2(a) = 1 - 3/4

cos^2(a) = 1/4

Taking the square root on both sides:

cos(a) = ±√(1/4)

Since cosine is positive in the first and fourth quadrants, we take the positive value:

cos(a) = √(1/4) = 1/2

2. Find tan(a): Using the identity tan(a) = sin(a) / cos(a), we can substitute the values we found:

tan(a) = (√3/2) / (1/2)

tan(a) = (√3/2) * (2/1)

tan(a) = √3

So, in this case:

cos(a) = 1/2 and tan(a) = √3.

б) Given sin(a) = 0.25

1. Find cos(a): Using the same identity as before:

cos^2(a) = 1 - sin^2(a)

cos^2(a) = 1 - (0.25)^2

cos^2(a) = 1 - 0.0625

cos^2(a) = 0.9375

Taking the square root on both sides:

cos(a) = ±√0.9375

Since cosine is positive in the first and fourth quadrants, we take the positive value:

cos(a) = √0.9375 ≈ 0.968

2. Find tan(a): Using the same tangent identity as before:

tan(a) = sin(a) / cos(a)

tan(a) = 0.25 / 0.968 ≈ 0.258

So, in this case:

cos(a) ≈ 0.968 and tan(a) ≈ 0.258.