Question

state the sign of 260°​

Answer 1

$\huge\mathbb\fcolorbox{blue}{lavenderblush}{★Answer★}$

Easiest method to work with trigonometry is two right-angle triangles.

First triangle has sides 1,1, sqrt(2) and angles 45, 45, 90 degrees.

sqrt(2)^2 = 1^2+1^2 = 2=1+1

This gives:

sin(45) = 1/sqrt(2) = 0.7071

cos(45) = 1/sqrt(2) = 0.7071

sin^2(45) and cos^2(45) are both 1/sqrt(2) * 1/sqrt(2) = 1/2

Second triangle has sides 1,sqrt(3),2 and angles 30,60,90

2^2 = 1^2+sqrt(3)^2 = 4=1+3

sin(30) = 1/2 = 0.5

cos(30) = sqrt(3)/2 = 0.866

sin(60) = sqrt(3)/2 = 0.866

cos(60) =1/2 = 0.5

hence

sin^2(30) and cos^2(60) are both 1/2 * 1/2 = 1/4

sin^2(60) and cos^2(30) are both sqrt(3)/2 * sqrt(3)/2 = 3/4

so the answer you want is

sin^2(6) = 3/4

also:

tan(45) = 1/1 = 1 and tan^2(45) = 1

tan(30) = 1/sqrt(3) = 0.57735 and tan^2(30) = 1/3

tan(60) = sqrt(3)/1 = 1.732 and tan^2(60) = 3

for completeness: sin^(x) + cos^2(x) = 1

this relationship can be used to swap between sin^2 and cos^2

$\huge\mathbb\fcolorbox{blue}{lavenderblush}{★ok★}$