Final answer:
To rewrite each function in terms of a trigonometric function of an angle within the interval [0,π/4] or [0°, 45°], we can use the unit circle and the trigonometric ratios of the angles within that interval. For each function given, we find an equivalent angle within the interval by subtracting or adding multiples of 360° until we get an angle between 0° and 45°.
Step-by-step explanation:
To rewrite each function in terms of a trigonometric function of an angle within the interval [0,π/4] or [0°, 45°], we can use the unit circle and the trigonometric ratios of the angles within that interval.
i. For sin 140°, we can find an equivalent angle within the given interval by subtracting 360° until we get an angle between 0° and 45°. 140° - 360° = -220°, -220° + 360° = 140°. Therefore, sin 140° is equivalent to sin 140° = sin (140° - 360°) = sin (-220°).
ii. For cos 105°, we can apply the same method. 105° - 360° = -255°, -255° + 360° = 105°. Therefore, cos 105° is equivalent to cos 105° = cos (105° - 360°) = cos (-255°).
iii. For cos 260°, we can again use the method. 260° - 360° = -100°, -100° + 360° = 260°. Therefore, cos 260° is equivalent to cos 260° = cos (260° - 360°) = cos (-100°).
iv. For tan (-11π/18), we can find the equivalent angle in degrees by converting the given radian measure. -11π/18 ≈ -196.666°. Since this angle is already within the given interval, we don't need to make any adjustments. Therefore, tan (-11π/18) remains the same.
v. For sec (-85)°, we need to find an equivalent angle within the given interval. -85° - 360° = -445°, -445° + 360° = -85°. Therefore, sec (-85)° is equivalent to sec (-85° - 360°) = sec (-445°).