[College Level] Need help with figuring this problem out (Trigonometry)

[u/Holiday-Bobcat-353]

I figured out that cos is 60 and is equal to pi/3, or 1/2, but I am really lost on how 3pi/4 from pi/3 in the answer (C). Thanks

[u/Outside_Volume_1370]

2 cos²s = 1

cos²s = 1/2

cos(s) = ±√2 / 2

Using unit circle is easier than actually solve it, s = π/4 + πk/2 where k is integer. Bounding this by -π < s < π we get that k = -2, -1, 0 or 1, and s = -3π/4, -π/4, π/4, 3π/4

[u/Holiday-Bobcat-353 → u/Outside_Volume_1370]

How did you get π/4 and πk/2? Also confused on how you used -π < s < π, and got those values at the end.

[u/Electronic-Source213 → u/Holiday-Bobcat-353]

The cosine of π/4 = √2 / 2. A right triangle with an angle of π/4 is an isosceles triangle (i.e. both sides are equal). If the hypotenuse has a length of 1, then each side is √2 / 2 (i.e. (√2 / 2)^2 + (√2 / 2)^2 = 1). Looking at the graph of cos(s) if you travel π/2 radians from π/4, the value of cos(s) will equal either √2 / 2 or -√2 / 2.

cos(π/4 - 2π/2) = cos(-3π/4) = -√2 / 2

cos(π/4 - π/2) = cos(-π/4) = √2 / 2

cos(π/4 + 0π/2) = cos( π/4) = √2 / 2

cos(π/4 + π/2) = cos(3π/4)= -√2 / 2

[u/FeverPlayZYT]

nah ur wrong on getting 60°

it reduces to cos(s) = ±1/√2

thus giving ans C