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Evaluate

3 \approx 1.732050808

Solution Steps

tan (\frac{4 π}{3})

Use

tan (x + y) = \frac{t a n ( x ) + t a n ( y )}{1 - t a n ( x ) t a n ( y )}

where

x = π

and

y = \frac{π}{3}

to obtain the result.

tan (π + \frac{π}{3}) = \frac{tan ( π ) + tan ( \frac{π}{3} )}{1 - tan ( π ) tan ( \frac{π}{3} )}

Get the value of

tan (π) \approx - 0

from trigonometric values table. Replace the value in both the numerator and the denominator.

\frac{0 + tan ( \frac{π}{3} )}{1 - 0 tan ( \frac{π}{3} )} \approx 1.732050808

Get the value of

tan (\frac{π}{3}) \approx 1.732050808

from trigonometric values table. Replace the value in both the numerator and the denominator.

\frac{0 + 3}{1 - 0 3} \approx 1.732050808

Do the calculations.

3 \approx 1.732050808

Quiz

10 problems similar to:

tan (\frac{4 π}{3})

Similar Problems from Web Search

How do you evaluate

tan (\frac{2 π}{3})

https://socratic.org/questions/how-do-you-evaluate-tan-2pi-3

tan (\frac{2 π}{3}) = - 3

tan (\frac{2 π}{3})

Recall the identity

tan θ = \frac{sin θ}{cos θ}

How do you evaluate

tan (\frac{5 π}{3})

https://socratic.org/questions/how-do-you-evaluate-tan-5pi-3

Alan P. Apr 26, 2015 The intersection of the ray for

\frac{5 π}{3}

with the unit circle is at the same place as the ray for

(- \frac{π}{3})

How do you evaluate

tan (\frac{8 π}{3})

https://socratic.org/questions/how-do-you-evaluate-tan-8pi-3

- 3

Explanation: Trig table and unit circle give -->

tan (\frac{8 π}{3}) = tan (\frac{2 π}{3} + \frac{6 π}{3}) = tan (\frac{2 π}{3} + 2 π) =

arctan (- 3 / 2)

doesn't give expected result.

https://math.stackexchange.com/questions/860565/arctan-3-2-doesnt-give-expected-result

By definition ,

arctan x

is the angle (in radians) between

- π / 2

π / 2

whose tangent is

x

. There are infinitely many numbers

y

tan y = - 3 / 2

How do I evaluate

tan (\frac{π}{3})

without using a calculator?

https://socratic.org/questions/how-do-i-evaluate-tan-pi-3-without-using-a-calculator

1

3

2

right angled triangle to find:

tan (\frac{π}{3}) = 3

How do you find the exact value of

tan (\frac{1 0 π}{3})

https://socratic.org/questions/how-do-you-find-the-exact-value-of-tan-10pi-3

tan (\frac{1 0 π}{3})

Explanation: On the trig unit circle,

tan (\frac{1 0 π}{3}) = tan (\frac{4 π}{3} + 2 π) = tan (\frac{π}{3}) = 3

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\tan(\pi +\frac{\pi }{3})=\frac{\tan(\pi )+\tan(\frac{\pi }{3})}{1-\tan(\pi )\tan(\frac{\pi }{3})}

Use \tan(x+y)=\frac{\tan(x)+\tan(y)}{1-\tan(x)\tan(y)} where x=\pi and y=\frac{\pi }{3} to obtain the result.

\frac{0+\tan(\frac{\pi }{3})}{1-0\tan(\frac{\pi }{3})}\approx 1.732050808

Get the value of \tan(\pi )\approx -0 from trigonometric values table. Replace the value in both the numerator and the denominator.

\frac{0+\sqrt{3}}{1-0\sqrt{3}}\approx 1.732050808

Get the value of \tan(\frac{\pi }{3})\approx 1.732050808 from trigonometric values table. Replace the value in both the numerator and the denominator.

\sqrt{3}\approx 1.732050808

Do the calculations.

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