Solve tan(5pi/8)

$$\tan ( \frac { 5 \pi } { 8 } )$$

Evaluate

$$-\left(\sqrt{2}+1\right)\approx -2.414213562$$

Solution Steps

Use \tan(x+y)=\frac{\tan(x)+\tan(y)}{1-\tan(x)\tan(y)} where x=\pi and y=\frac{\pi }{4} to obtain the result.

$$\tan(\pi +\frac{\pi }{4})=\frac{\tan(\pi )+\tan(\frac{\pi }{4})}{1-\tan(\pi )\tan(\frac{\pi }{4})}$$

Get the value of \tan(\pi ) from trigonometric values table. Replace the value in both the numerator and the denominator.

$$\frac{0+\tan(\frac{\pi }{4})}{1-0\tan(\frac{\pi }{4})}$$

Get the value of \tan(\frac{\pi }{4}) from trigonometric values table. Replace the value in both the numerator and the denominator.

$$\frac{0+1}{1-0\times 1}$$

Do the calculations.

$$1$$