+37157 cos (theta) = adj/hyp = 2 sqrt6 / 2 sqrt 15 = sqrt6/sqrt15
arc cos(sqrt6/sqrt15) = 50.8 degrees
(sin -2pi/3 / cos (-2pi/3) ) / sin (7pi/4) - sec (-pi)
-sqrt2/3 / -1/2 / sqrt2/2 - 1 /cos pi
2 sqrt2 /3 / sqrt2/2 + 1
4/3 + 1 = 1 4/3
+130071 tan (-2pi/3)
__________ - sec (- pi)
sin (7pi/4)
One step at a time.....
tan (-2pi/3) = tan (-120°) = tan (360 - 120)° = tan (240°) = tan (60°) = √3
sin (7pi/4) = sin (-pi/4) = -sin (pi/4) = - sin (45°) = - √2/2
sec (-pi) = sec (pi) = sec (180°) = -1
So....putting this all together we get
√3 / [ -√2/2 ] - (-1) =
2√3 / -√2 + 1 =
2√3√2 / [ - √2 * √2 ] + 2/2 =
-2√6 / 2 + 2/2 =
-√6 + 1
