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Let alpha be an angle in the third quadrant such that tan alpha = \(4/7\).  Compute cos alpha.

 Apr 27, 2022

Best Answer 

 #1
avatar+23183 
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Since  tan = y / x  and both the  x  value and the  y  value are negative in the third quadrant,

                               y = -4  and  x = -7.

 

Since  r = sqrt( x2 + y2 )    --->     r = sqrt( (-7)2 + (-4)2 )     --->     r = sqrt( 65 )

 

Since  cos = x / r    --->     cos = -7 / sqrt( 65 )

 Apr 27, 2022
 #1
avatar+23183 
+1
Best Answer

Since  tan = y / x  and both the  x  value and the  y  value are negative in the third quadrant,

                               y = -4  and  x = -7.

 

Since  r = sqrt( x2 + y2 )    --->     r = sqrt( (-7)2 + (-4)2 )     --->     r = sqrt( 65 )

 

Since  cos = x / r    --->     cos = -7 / sqrt( 65 )

geno3141 Apr 27, 2022

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