Cho sinx = -3/45. Tính

Given \( \sin(x) = -\frac{3}{45} \), we need to evaluate the sine function for various arguments using trigonometric identities. Let's break down each part:

a) \(\sin(-x)\)
\[ \sin(-x) = -\sin(x) = -\left(-\frac{3}{45}\right) = \frac{3}{45} \]

b) \(\sin(x - 7\pi)\)
\[ \sin(x - 7\pi) = \sin(x + \pi - 8\pi) = \sin(x - \pi) = -\sin(x) = -\left(-\frac{3}{45}\right) = \frac{3}{45} \]

c) \(\sin(x + 10\pi)\)
\[ \sin(x + 10\pi) = \sin(x + 2 \cdot 5\pi) = \sin(x) = -\frac{3}{45} \]

d) \(\sin(-x - 5\pi)\)
\[ \sin(-x - 5\pi) = \sin(-(x + 5\pi)) = -\sin(x + 5\pi) = -\sin(x) = -\left(-\frac{3}{45}\right) = \frac{3}{45} \]

e) \(\sin(11\pi - x)\)
\[ \sin(11\pi - x) = \sin(\pi - (12\pi - x)) = \sin(\pi - x) = \sin(x) = -\frac{3}{45} \]

f) \(\sin(8\pi - x)\)
\[ \sin(8\pi - x) = \sin(- (x - 8\pi)) = -\sin(x - 8\pi) = -\sin(x) = -\left(-\frac{3}{45}\right) = \frac{3}{45} \]

So, the values of each are as below:

a) \(\sin(-x) = \frac{3}{45} \)
b) \(\sin(x - 7\pi) = \frac{3}{45} \)
c) \(\sin(x + 10\pi) = -\frac{3}{45} \)
d) \(\sin(-x - 5\pi) = \frac{3}{45} \)
e) \(\sin(11\pi - x) = -\frac{3}{45} \)
f) \(\sin(8\pi - x) = \frac{3}{45} \)