Question

Find each exact function value. ​See Example 3.​tan (-14π/ 3)

Accepted Answer

First, recognize that the tangent function has a period of $$\pi$$, meaning $$	an(	heta) = 	an(	heta + k\pi)$$ for any integer $$k. $$This allows us to simplify the angle by adding or subtracting multiples of $$\pi. $$Start by simplifying the angle $$-\frac{14\pi}{3}. $$Since the period is $$\pi = \frac{3\pi}{3}$$, find an integer $$k$$ such that $$-\frac{14\pi}{3} + k\pi$$ lies within a standard interval, for example between $$-\pi$$ and $$\pi or $$between $$0$$ and $$2\pi. $$Calculate $$k by $$dividing $$-\frac{14}{3} by$$ $$1 ($$since the period in terms of $$\pi is 1$$), and find the closest integer to add multiples of $$\pi to $$bring the angle into a simpler equivalent angle. For instance, add $$5\pi = \frac{15\pi}{3} to$$ $$-\frac{14\pi}{3} to $$get a positive angle. After simplification, express the resulting angle in terms of a known angle on the unit circle, such as $$\frac{\pi}{3}$$, $$\frac{2\pi}{3}$$, etc., to find the exact value of the tangent function using known tangent values. Finally, use the identity $$	an(	heta) = \frac{\sin(	heta)}{\cos(	heta)}$$ and the known sine and cosine values for the simplified angle to write the exact value of $$	an(-\frac{14\pi}{3}).$$

Find each exact function value. See Example 3.
tan (-14π/ 3)

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Angle Reduction Using Coterminal Angles

Tangent Function Properties and Periodicity

Exact Values of Tangent for Special Angles