Question

Найдите sina если tga=-2 и cosa>0

Answer 1

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Answer 2

To find the value of sin(a), we can use the trigonometric identity:

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

Given that tga = -2 and cosa > 0, we can use the following definitions:

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

And since cosa > 0, we know that cos(a) is positive, so we can safely divide by it.

Now, let's substitute the given value of tga:

tga = -2 = sin(a) / cos(a)

Now, we can solve for sin(a):

sin(a) = tga * cos(a) sin(a) = -2 * cos(a)

We also know that sin^2(a) + cos^2(a) = 1, so we can replace sin^2(a) with (1 - cos^2(a)):

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

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

Now, solve for cos^2(a):

cos^2(a) = 1 - 1 cos^2(a) = 0

Taking the square root of both sides:

cos(a) = ±√0 cos(a) = 0

Since cos(a) is positive according to the given information (cosa > 0), we have:

cos(a) = 0

Now, let's find sin(a):

sin(a) = -2 * cos(a) sin(a) = -2 * 0 sin(a) = 0

So, the value of sin(a) is 0.