SOLUTION: If tan(x) = −40/9 and x is in quadrant IV, with 0° ≤ x < 360°, find the exact values of the expressions without solving for x. (a) sin(x/2) (b) cos(x/2) (c) tan

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Question 1204118: If tan(x) = −40/9 and x is in quadrant IV, with 0° ≤ x < 360°, find the exact values of the expressions without solving for x.
(a) sin(x/2)

(b) cos(x/2)

(c) tan(x/2)


Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52873)   (Show Source): You can put this solution on YOUR website!
.
If tan(x) = −40/9 and x is in quadrant IV, with 0° ≤ x < 360°, find the exact values of the expressions without solving for x.
(a) sin(x/2)
(b) cos(x/2)
(c) tan(x/2)
~~~~~~~~~~~~~~~~~~~~~~~~~~ 

If tan(x) = −40/9 and x is in quadrant IV, then it means that 

    the opposite leg is 40 units, the adjacent leg is 9 units and the hypotenuse is   =  = 41 unit.

It implies that  cos(x) = .


Next, use the formulas for half argument


     =  =  =  = ;


     =  =  =  = ;


     = .

Solved.



Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!




also,



then => ,
=>

then



(a)

using Half Angle Formulas



or
sin is negative in Q IV



(b)





...cos is positive in Q IV


(c)




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