Question

Tgα=4 0<α<Π:2 Найти: sinα, cosα, ctgα

Answer 1

Tg принадлежит 1 четв., sin>0, cos>0, ctg>0
ctg t=0.25
sin t=tg^2t/(1+tg^2t)=4^2/(1+4^2)=16/17 примерно равно 0.9
cos t=ctg t* sin t=4*0.9=3.6
наверное так

Answer 2

To find the values of sine (sin α), cosine (cos α), and cotangent (ctg α) of an angle α, given that tan α = 4 and 0 < α < π/2, we can use the following trigonometric relationships:

1. sin α = tan α / √(1 + tan² α)
2. cos α = 1 / √(1 + tan² α)
3. ctg α = 1 / tan α

Let's calculate each value step by step:

1. sin α = tan α / √(1 + tan² α) Plugging in the value of tan α = 4: sin α = 4 / √(1 + 4²) sin α = 4 / √(1 + 16) sin α = 4 / √17 (exact value)

2. cos α = 1 / √(1 + tan² α) Plugging in the value of tan α = 4: cos α = 1 / √(1 + 4²) cos α = 1 / √(1 + 16) cos α = 1 / √17 (exact value)

3. ctg α = 1 / tan α Plugging in the value of tan α = 4: ctg α = 1 / 4 (exact value)

So, the values are: sin α = 4 / √17 (exact value) cos α = 1 / √17 (exact value) ctg α = 1 / 4 (exact value)

Note: If you need the approximate decimal values, you can use a calculator to evaluate the square roots and perform the divisions.