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How do you sketch $θ = \frac{7 π}{4}$ $theta=(7pi)/4$ in standard position?

1 Answer

Jul 29, 2015

$2 π = \frac{8 π}{4}$ $2pi = (8pi)/4$ is one full revolution
$\to \frac{7 π}{4}$ $rarr (7pi)/4$ is $\frac{π}{4}$ $pi/4$ less than a full revolution.

Explanation:

...to look at it another way:

$\frac{π}{2}$ $pi/2$ is a right angle

$\frac{7 π}{4} = 3 \cdot (\frac{π}{2}) + \frac{1}{2} \cdot \frac{π}{2}$ $(7pi)/4 = 3*(pi/2) + 1/2*pi/2$
$XXXX$ $color(white)("XXXX")$ is 3 right-angles plus half a right angle
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