How do you determine #tantheta# given #sintheta=-1/3, 180^circ<theta<270^circ#?

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How do you determine #tantheta# given #sintheta=-1/3, 180^circ<theta<270^circ#?

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Answer 1 · 2016-12-16T01:00:55

#tan(theta)=1/(2sqrt(2))#

Explanation:

If #180^@ < theta < 270^@#
and #sin(theta)=-1/3#
then
enter image source here
The adjacent side is calculated using the Pythagorean Theorem as
#-sqrt(3^2-1^2)=-2sqrt(2)#
Givin
#tan(theta)="opposite"/"adjacent"=((-1))/((-2sqrt(2)))= 1/(2sqrt(2)#

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How do you determine #tantheta# given #sintheta=-1/3, 180^circ<theta<270^circ#?

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