SOLUTION: Hi there! How can I answer this question? Please explain to me the solution so I will know how to answer it next time. Find cos theta, tan theta and sec theta, if sin theta = -8

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Question 644165: Hi there! How can I answer this question? Please explain to me the solution so I will know how to answer it next time.
Find cos theta, tan theta and sec theta, if sin theta = -8/17 and 180< theta < 270.
thank you soooooo much!
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
Find cos theta, tan theta and sec theta, if sin theta = -8/17 and 180< theta < 270
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use x for theta
O for opposite side
A for adjacent side
H for hypotenuse
working with reference angle x in quadrant III where sin and cos<0
..
sinx=-8/17=O/H
O=-8
H=17
By the Pythagorean Theorem
A=-√(H^2-O^2)=-√(17^2-8^2)=-√(289-64)=-√225=-15
cosx=A/H=-15/17 (in quadrant III where cos<0)
tanx=O/A=-8/-15=8/15 (in quadrant III where tan>0)
secx=H/A=-17/15 (in quadrant III where sec<0)
..
An alternate method is to do it algebraically:
sin^2x+cos^2x=1
cos^2x=1-sin^2x
cosx=√(1-sin^2x)=√(1-(8/17)^2)=√(1-64/289)=√(225/289=15/17
cosx=-15/17 in quadrant III
secx=-17/15
tanx=sinx/cosx=8/15