Question

4+5 tg^2x cos^2x , sin x=0.4

Answer 1

$4+5tg^2 x *cos^2 x=4+5sin^2 x=4+5*0.4^2=4+5*0.16=4+0.8=4.8$

Answer 2

To find the value of the expression 4 + 5tg^2(x)cos^2(x) when sin(x) = 0.4, we can use the given value of sin(x) to find the values of cos(x) and tg(x) (tangent of x).

Given that sin(x) = 0.4, we can use the Pythagorean identity to find cos(x):

cos^2(x) = 1 - sin^2(x) cos^2(x) = 1 - 0.4^2 cos^2(x) = 1 - 0.16 cos^2(x) = 0.84

Taking the square root of both sides, we get:

cos(x) ≈ ±√(0.84)

Since cos(x) can be positive or negative, we consider both possibilities. Let's calculate the values of cos(x):

cos(x) ≈ ±√(0.84) cos(x) ≈ ±0.917

Now, let's calculate the value of tg(x):

tg(x) = sin(x)/cos(x) tg(x) = 0.4/0.917 tg(x) ≈ 0.436

Now, we can substitute these values into the given expression:

4 + 5tg^2(x)cos^2(x) 4 + 5(0.436)^2(0.917)^2 4 + 5(0.190496)(0.841489) 4 + 5(0.160207) 4 + 0.801035 4.801035

Therefore, when sin(x) = 0.4, the value of the expression 4 + 5tg^2(x)cos^2(x) is approximately 4.801.