Question

exact value for sin 3pi/4 - tan 5pi/6

Answer 1

\[\sin3\pi/4 = \sqrt{2}/2\] while \[\tan5\pi/6 = -\sqrt{3}/3\]

Answer 2

how did you get those values though? :l

Answer 3

use these triangles to help. the reference angle for \[\sin \pi/4\]is ALWAYS \[1/\sqrt{2}\] or \[\sqrt{2}/2\] if you rationalized it. Since \[\sin 3\pi/4\] is in the 2nd quadrant, sine is positive, so the answer is just \[1/\sqrt{2}\] .

the reference angle for \[\tan \pi/6\] is ALWAYS \[1/\sqrt{3}\] and since \[\tan 5\pi/6\] is in the 2nd quadrant, tan is negative, thus the answer is \[-1/\sqrt{3}\] or \[-\sqrt{3}/3\] if you rationalized it.