Question

1) sin 510°                   A) - frac{1}{2} 2) cos 690°                Б) - frac{\sqrt{3}}{2} 3)cos 840°               В) frac{\sqrt{3}}{2} 4)960°                     Г) frac{\sqrt{2}}{2}                                  Д) frac{1}{2}

Answer 1

$sin510^\circ =sin(360^\circ +150^\circ )=sin(180^\circ -30^\circ )=\\\\=sin30^\circ =\frac{1}{2}\\\\cos690^\circ =cos(2\cdot 360^\circ -30^\circ )=cos30^\circ =\frac{\sqrt3}{2}\\\\cos840^\circ =cos(2\cdot 360^\circ +120^\circ )=cos(180^\circ -60^\circ )=\\=-cos60^\circ =-\frac{1}{2}\\\\sin960^\circ =sin(2\cdot 360^\circ +240^\circ )=sin(270^\circ -30^\circ )=\\=-cos30^\circ =-\frac{\sqrt3}{2}$

Answer 2

To find the trigonometric values of the given angles, we need to first convert the angles to their equivalent angles within one full revolution (360°). We can do this by subtracting or adding multiples of 360° until we get an angle between 0° and 360°. Then, we can use the unit circle or trigonometric identities to find the trigonometric values.

Let's evaluate each angle:

1. sin 510°: We can subtract 360° once from 510° to get an equivalent angle within one full revolution: 510° - 360° = 150°.

Now, the angle is 150°. Looking at the unit circle, we can find that sin 150° = 1/2.

So, the correct answer is A) 1/2.

2. cos 690°: We can subtract 360° once from 690° to get an equivalent angle within one full revolution: 690° - 360° = 330°.

Now, the angle is 330°. Looking at the unit circle, we can find that cos 330° = √3/2.

So, the correct answer is Б) √3/2.

3. cos 840°: We can subtract 360° twice from 840° to get an equivalent angle within one full revolution: 840° - 2 * 360° = 120°.

Now, the angle is 120°. Looking at the unit circle, we can find that cos 120° = -1/2.

So, the correct answer is Д) -1/2.

4. 960°: We can subtract 360° twice from 960° to get an equivalent angle within one full revolution: 960° - 2 * 360° = 240°.

Now, the angle is 240°. Looking at the unit circle, we can find that cos 240° = -√3/2.

So, the correct answer is Г) -√3/2.