Question

Алгебра найти cos a, если sin а =-4÷5; П<а<3П÷2

Answer 1

$Sin\alpha=-\frac{4}{5}\\\\\pi$

Answer 2

To find cos(a), we can use the Pythagorean trigonometric identity:

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

We are given that sin(a) = -4/5, so we can calculate sin^2(a):

sin^2(a) = (-4/5)^2 = 16/25.

Now, using the Pythagorean identity:

cos^2(a) = 1 - sin^2(a) = 1 - 16/25 = 9/25.

Finally, taking the square root of both sides:

cos(a) = ±√(9/25).

Remember that the value of cos(a) depends on the quadrant in which angle "a" lies. Given the interval 0 < a < 3π/2, angle "a" is in the second quadrant, where cosine is negative. Therefore,

cos(a) = -√(9/25) = -3/5.