Question

PLEASE HELP ASAP

Answer 1

B

Step-by-step explanation: edg

Answer 2

The tan is negative in the 2nd and 4th quadrants, knowing this, the angle that equals the value that tan = 1 in the first quadrant is the tan 45° = 1, but the question restrict for 3pi/2 < theta < 2pi, so it's the same as 270° < theta < 360° (4° Quadrant), then moving the tan 45° = to this quadrant the value will be negative, tan in 4°Q = tan(360 - 45=315°) = -1.

sec theta = 1/cos theta

cos 45° =
$\sqrt{2} \div 2$

cos values in 4°Q will be positives, so it doesn't change the signal.

sec 315° = 1/cos 315°
sec 315° = 1/square root (2)/2
sec 315 = 1/1 x 2/sqroot(2)
$sec \: 315 = 2 \div \sqrt{2}$
$sec \: 315 = (2 \div \sqrt{2}) \: \times ( \sqrt{2} \div \sqrt{2})$
$sec \: 315 = 2 \sqrt{2} \div 2$
$sec \: 315 = \sqrt{2}$