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assume that a i an angle in standard position whose terminal side contains the point...

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mpumpkin | Salutatorian

Posted October 27, 2013 at 10:20 PM via web

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assume that a i an angle in standard position whose terminal side contains the point (-2,-sqrt2). find the exact values of the functions:

sina a

cos a

tan a

sec a

csc a

cot a

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flbyrne | (Level 3) Assistant Educator

Posted October 27, 2013 at 11:21 PM (Answer #1)

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Because both coordinates are negative, angle a is in the third quadrant, and the distance of point (-2,`-sqrt2`) to the origin can be calculated using the Pythagorean theorem.

`d=sqrt(2^2+sqrt2^2)=sqrt6`

`sina=y/d=(-sqrt2)/sqrt6=-0.5774`

`cosa=x/d=-2/sqrt6=-0.8165`

`tana=y/x=(-sqrt2)/(-2)=0.7071`

`seca=d/y=sqrt6/(-sqrt2)=-1.7321`

`coseca=d/x=sqrt6/(-2)=-1.2247`

`cotana=x/y=(-2)/(-sqrt2)=1.4142`

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