Question

13. sin150° - 5 cos 300° + 7 tan 225°/tan135° + 3 sin 210°
1) 1
2) 2
3)-2​

Answer 1

150 lis in quadrant II whose reference angle is 30; sin is positive in quadrant II

sin (150) = sin(30) =1/2

300 is in quadrant IV whose reference angle is 60; cos is positive in quadrant IV

cos(300)= cos(60) = 1/2

225 is in quadrant III whose reference angle is 45 ;tan is positive in quadrant III

tan(225) = tan(45)=1

135 is in quadrant II whose reference angle is 45 ;tan is negative in quadrant II

tan(135) = -tan(45)=-1

210 is in quadrant III whose reference angle is 30 ;sin is negative in quadrant III

sin(210) = -sin(30)=-1/2

sin 150 = 1/2

cos 300 = 1/2

tan 225 = 1

tan 135 = -1

sin 210 = -1/2

[Sin150 degress-5cos 300 degrees+7 tan 225 degrees] / [tan 135 degrees + 3 sin 210 degrees]

= (1/2-5/2+7) / (-1-3/2)

= 5 / (-5/2)

= -2