Question

Найти sin²a, если tg a = -2/15 , π/2<а<π

Answer 1

To find sin²a, we first need to find the value of sin a using the given information that tan a = -2/15 and π/2 < a < π.

We know that tan a = sin a / cos a, so we can write:

sin a / cos a = -2/15

Next, we can use the trigonometric identity: sin²a + cos²a = 1

Rearrange the equation to isolate sin a:

sin a = (-2/15) * cos a

Now, we can use the fact that π/2 < a < π to determine the sign of cos a. In the second quadrant (π/2 < a < π), both sin a and cos a are negative.

Now, we can use the Pythagorean trigonometric identity sin²a + cos²a = 1 to find sin²a:

sin²a + cos²a = 1 ((-2/15) * cos a)² + cos²a = 1

Let's solve for cos a:

(4/225) * cos²a + cos²a = 1 (4/225 + 1) * cos²a = 1 (229/225) * cos²a = 1

Now, isolate cos²a:

cos²a = 225 / 229

Finally, find sin²a using sin²a + cos²a = 1:

sin²a = 1 - cos²a sin²a = 1 - (225 / 229) sin²a = (229 - 225) / 229 sin²a = 4 / 229

So, sin²a = 4 / 229.