Question

Найдите sinA, если cosA = -7/25 и A € (pi; 3pi/2)

Answer 1

$cosA=-\frac{7}{25}\\\\A\in (\pi ,\frac{3\pi }{2})\; \; \Rightarrow \; \; sinA$

Answer 2

т.к. a ∈ (π; 3π/2) ⇒ sin a имеет отрицательное значение

$\sin a=\pm\sqrt{1-\cos^{2}a}=-\sqrt{1-\cos^{2}a}=-\sqrt{1-(-\frac{7}{25})^{2}}=-\sqrt{1-\frac{49}{625}}=-\sqrt{\frac{576}{625}}=-{\frac{24}{25}$

Ответ: -24/25

Answer 3

To find sin(A) given that cos(A) = -7/25 and A ∈ (π, 3π/2), we can use the Pythagorean trigonometric identity:

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

Since we know the value of cos(A), we can solve for sin(A):

sin^2(A) + (-7/25)^2 = 1

sin^2(A) + 49/625 = 1

sin^2(A) = 1 - 49/625

sin^2(A) = 576/625

Now, take the square root of both sides to get the value of sin(A):

sin(A) = ±√(576/625)

sin(A) = ±(√576)/(√625)

sin(A) = ±24/25

Since A lies in the interval (π, 3π/2), the sine function is negative in that range. So, sin(A) = -24/25.

Therefore, sin(A) = -24/25.