Question

sin75/3-4cos^2(5)

Answer 1

$$\sin \frac {75}{3} - 4 \cos^ {2} 5$$

Solution.

Transform the first term

$$\sin \frac {75}{3} - 4 \cos^ {2} 5 = \sin 25 - 4 \cos^ {2} 5$$

Use tables of sine and cosine:

$$\sin 25 \approx \sin (8\pi - 0.13) = - \sin 0.13 \approx -0.13$$ $$\cos 5 \approx \cos (2\pi - 1.28) = \cos 1.28 \approx 0.29$$

Then finally compute:

$$\sin 25 - 4 \cos^ {2} 5 \approx - 0.13 - 4 \cdot 0.29^ {2} = - 0.4664$$

Answer: -0.4664