Question

Зная, что sinα + cosα = 0,6. Найдите sinα · cosα

Answer 1

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Answer 2

To find the value of sinα · cosα, we can use trigonometric identities to express sinα and cosα in terms of their sum (sinα + cosα).

Given that sinα + cosα = 0.6, we can square this equation to get:

(sinα + cosα)^2 = (0.6)^2

Expanding the left-hand side using the identity (a + b)^2 = a^2 + 2ab + b^2, we get:

sin^2α + 2sinαcosα + cos^2α = 0.36

Now, we'll use the trigonometric identity sin^2α + cos^2α = 1:

1 + 2sinαcosα = 0.36

Now, isolate the term with sinα · cosα:

2sinαcosα = 0.36 - 1

2sinαcosα = -0.64

Finally, divide both sides by 2:

sinα · cosα = -0.32

So, the value of sinα · cosα is -0.32.