Find the value of given trigonometric function.Round your answer to four decimal places. $\tan \frac { \pi } { 8 }$
A) $\tan \frac { \pi } { 8 } \approx$ 0.3142
B) $\tan \frac { \pi } { 8 } \approx$ 0.6142
C) $\tan \frac { \pi } { 8 } \approx$ - 0.4142
D) $\tan \frac { \pi } { 8 } \approx$ 0.4142
E) $\tan \frac { \pi } { 8 } \approx$ 0.5142

Question

Find the value of given trigonometric function.Round your answer to four decimal places.​ $\tan \frac { \pi } { 8 }$ ​
A) $\tan \frac { \pi } { 8 } \approx$ 0.3142
B) $\tan \frac { \pi } { 8 } \approx$ 0.6142
C) $\tan \frac { \pi } { 8 } \approx$ - 0.4142
D) $\tan \frac { \pi } { 8 } \approx$ 0.4142
E) $\tan \frac { \pi } { 8 } \approx$ 0.5142

Quizplus · Accepted Answer

Using the trigonometric identity $\cos(2	heta) = 1-2\sin^2(	heta)$, we have 
$$\cos\left(\frac{\pi}{4}ight) - \sin\left(\frac{\pi}{4}ight)\cos\left(\frac{\pi}{2}ight)$$ 
$$= \frac{1}{\sqrt{2}} - \frac{1}{\sqrt{2}}\cdot0$$
$$= \frac{1}{\sqrt{2}}.$$

Rounding to four decimal places, we get 0.4142. Therefore, the best choice is D.

Find the Value of Given Trigonometric Function tan⁡π8\tan \frac { \pi } { 8 }tan8π​

Find the Value of Given Trigonometric Function $\tan \frac { \pi } { 8 }$