How do you evaluate if possible the 6 trigonometric functions of the real number $t = \frac{7 π}{6}$ $t= (7pi)/6$ ?

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How do you evaluate if possible the 6 trigonometric functions of the real number $t = \frac{7 π}{6}$ $t= (7pi)/6$ ?

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Answer 1 · 2016-04-11T08:23:44

$sin (\frac{7 π}{.6})) = - \frac{1}{2}, cos (\frac{7 π}{6}) = - \frac{\sqrt{3}}{2} and tan (\frac{7 π}{6}) = \frac{1}{\sqrt{3}}$ $sin ((7pi)/.6))=-1/2, cos ((7pi)/6)= -sqrt3/2 and tan ((7pi)/6)=1/sqrt3$ .
The recprocals, $csc (\frac{7 π}{.6})) = - 2, sec (\frac{7 π}{6}) = - \frac{2}{\sqrt{3}} and cot (\frac{7 π}{6}) = \sqrt{3}$ $csc ((7pi)/.6))=-2, sec ((7pi)/6)= -2/sqrt3 and cot ((7pi)/6)=sqrt3$ ...

Explanation:

In the third quadrant, both sine and cosine are negative and the tangent is positive.

$7 \frac{π}{6}$ $7pi/6$ direction is in the third quadrant.

For any of the six functions $f (θ)$ $f(theta)$ , $f (π + θ) = \pm f (θ) and 7 \frac{π}{6} = π + \frac{π}{6}$ $f(pi+theta)=+-f(theta) and 7pi/6=pi+pi/6$ .

So, in every case it is $\pm f (\frac{π}{6})$ $+-f(pi/6)$ .
Choose appropriate sign and prefix to $f (\frac{π}{6})$ $f(pi/6)$ . ..

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How do you evaluate if possible the 6 trigonometric functions of the real number $t = \frac{7 π}{6}$ $t= (7pi)/6$ ?

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How do you evaluate if possible the 6 trigonometric functions of the real number t= (7pi)/6t=7π6t= (7pi)/6?

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Explanation:

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How do you evaluate if possible the 6 trigonometric functions of the real number $t = \frac{7 π}{6}$ $t= (7pi)/6$ ?