cos (x/2) = -sqrt2/2 in (0,360) looking for two values ?? Can someone please help me I can’t seem to figure out how to solve thi

Question

3 years ago

10

s problem, I’m looking at other examples but I’m still confused please help

1 answer:

ValentinkaMS [17] · Answer 1 · 2022-09-29T18:18:39+03:00

Answer:

135° and 225°

Step-by-step explanation:

basically you want to find the value of x between 0 and 360 in this equation

cos x/2 = -(√2)/2

assume x/2 as n, so

cos n = -(√2)/2

n = 45°

then remember the quadrant system

0-90 1st quadrant, all is POSITIVE

90-180 2nd quadrant, only SIN has positive value

180 - 270 3rd quadrant, only TAN has positive value

270 -360 4th quadrant, only COS positive here.

so if you try to find negative value look into 2nd and 3rd quadrant that related 45° to x-axis (0°or 180°)

so the value of x is

180 - 45 = 135° (2nd quadrant) and

180 + 45° = 225° (3rd quadrant)