Question

Cos480°=...;tg(-315°)=...;ctg690°=... .

Answer 1

Cos480=cos(360+120)=cos120=cos(90+30)=-sin30=-1/2
tg(-315)= tg(-315 + 360)=tg 45=1
ctg690=- √3

Answer 2

To find the values of the trigonometric functions for the given angles, let's break them down into simpler angles using periodicity and symmetry properties of trigonometric functions.

1. cos(480°): We can rewrite 480° as a multiple of 360° plus an angle within the first revolution: 480° = 1 * 360° + 120°. Since the cosine function has a period of 360°, we can find the value of cos(120°). In the first quadrant, cos(120°) = cos(120° - 360°) = cos(-240°). Using the symmetry property, cos(-240°) = cos(240°). In the fourth quadrant, cos(240°) = -cos(240° - 360°) = -cos(-120°) = -cos(120°). Therefore, cos(480°) = -cos(120°) = -cos(120° - 360°) = -cos(-240°) = -cos(240°) = -cos(240° - 360°) = -cos(-120°) = -cos(120°).

2. tan(-315°): We can rewrite -315° as a multiple of 360° plus an angle within the first revolution: -315° = -1 * 360° + 45°. Since the tangent function has a period of 180°, we can find the value of tan(45°). In the first quadrant, tan(45°) = tan(45° - 180°) = tan(-135°). Using the symmetry property, tan(-135°) = -tan(135°). Therefore, tan(-315°) = -tan(45°) = -tan(45° - 180°) = -tan(-135°) = -(-tan(135°)) = tan(135°).

3. cot(690°): We can rewrite 690° as a multiple of 360° plus an angle within the first revolution: 690° = 1 * 360° + 330°. Since the cotangent function has a period of 180°, we can find the value of cot(150°). In the second quadrant, cot(150°) = -cot(150° - 180°) = -cot(-30°). Using the symmetry property, cot(-30°) = cot(30°). Therefore, cot(690°) = cot(150°) = -cot(150° - 180°) = -cot(-30°) = -cot(30°).

In summary:

• cos(480°) = -cos(120°)
• tan(-315°) = tan(135°)
• cot(690°) = -cot(30°)

Please note that the values provided are based on the standard trigonometric functions.