76. Приведите к тригонометрической функции угла α: 1) sin(+a): 2) 1g (π + α); 3) cos (2n + a); 4) tg (90°-α); 7) sin (π + α); 6) ctg (π-α); 8) cos (90° + a); 10) cos (α-π); 11) ctg (a-360°); 12) tg (-a +270°).

Решение:

• 1) \( \sin(\frac{\pi}{2} + \alpha) = \cos(\alpha) \)
• 2) \( \tan(\pi + \alpha) = \tan(\alpha) \)
• 3) \( \cos(2\pi + \alpha) = \cos(\alpha) \)
• 4) \( \tan(90^\circ - \alpha) = \tan(\frac{\pi}{2} - \alpha) = \cot(\alpha) \)
• 5) \( \cos(\frac{3\pi}{2} - \alpha) = -\sin(\alpha) \)
• 6) \( \cot(\pi - \alpha) = -\cot(\alpha) \)
• 7) \( \sin(\pi + \alpha) = -\sin(\alpha) \)
• 8) \( \cos(90^\circ + \alpha) = \cos(\frac{\pi}{2} + \alpha) = -\sin(\alpha) \)
• 9) \( \sin(\alpha - \frac{\pi}{2}) = -\cos(\alpha) \)
• 10) \( \cos(\alpha - \pi) = -\cos(\alpha) \)
• 11) \( \cot(\alpha - 360^\circ) = \cot(\alpha) \)
• 12) \( \tan(-\alpha + 270^\circ) = \tan(-\alpha + \frac{3\pi}{2}) = \cot(\alpha) \)