difficult math 004 10pts!

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12a)

Yes , ARB is a straight line since R is the touching point of circles with center A & B.

b)

ㄥPAR = 2ㄥPQS = 2*40 = 80°
;

ㄥPAR + ㄥTBR + ㄥAPT + ㄥBTP = 360°

80° + ㄥTBR + 90° + 90° = 360°
ㄥTBR = 100°

ㄥTSQ = (1/2)ㄥTBR = 100/2 = 50°




13a) sinθ / tanθ < 0 ,

sinθ > 0 and tanθ < 0
The terminal side in the 2nd quadrant.
or sinθ < 0 and tanθ > 0 ,
The terminal side in the 3rd quadrant.

b) tanθ / cosθ > 0 ,

tanθ > 0 and cosθ > 0
The terminal side in the 1st quadrant , but not on the y-axis since cosθ<>0
or tanθ < 0 and cosθ < 0 ,
The terminal side on the 2nd quadrant , but not on the y-axis since cosθ<>0.

c) cosθ sinθ < 0 ,

cosθ < 0 and sinθ > 0
The terminal side in the 2nd quadrant,
or cosθ > 0 and sinθ < 0 ,
The terminal side in the 4th quadrant.