Question

Sin a * cos a = 0,48 a острый кут найти sin a + cos a =

Answer 1

Объяснение:

(sin a + cos a) ²=sin² a +2sin a *cos a +cos² a=1+2*0,48=1,96

(sin a + cos a) ²=1,96

sin a + cos a=1,4

Answer 2

To find the value of sin a + cos a given that sin a * cos a = 0.48 and a is an acute angle, we can use the following approach:

Let's start by using the identity sin^2(a) + cos^2(a) = 1.

We can rearrange this equation to solve for cos^2(a):

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

Now, substitute the value of sin a * cos a into the equation:

cos^2(a) = 1 - (0.48)^2 cos^2(a) = 1 - 0.2304 cos^2(a) = 0.7696

Taking the square root of both sides:

cos(a) = sqrt(0.7696) cos(a) ≈ 0.8779

Since a is an acute angle, both sin(a) and cos(a) are positive.

Now, let's find sin(a):

sin^2(a) = 1 - cos^2(a) sin^2(a) = 1 - 0.8779^2 sin^2(a) = 1 - 0.7703 sin^2(a) ≈ 0.2297

Taking the square root of both sides:

sin(a) = sqrt(0.2297) sin(a) ≈ 0.4795

Therefore, sin(a) + cos(a) is approximately:

sin(a) + cos(a) ≈ 0.4795 + 0.8779 sin(a) + cos(a) ≈ 1.3574