[3 pi}/4 3π4 is 135^circ = 3 times 45^circ 135∘=3×45∘
Of course 30/60/90 and 45/45/90 are the only two triangles students are expected to know "exactly." We have to know the multiples of these triangles in the other quadrant. Here we have 45/45/90 in the second quadrant.
We start from cos(45^circ)=sin(45^circ)=1/sqrt{2}cos(45∘)=sin(45∘)=1√2. The angle 135^circ135∘ is supplementary to 45^circ45∘, so has the opposite cosine and the same sine.
cos({3pi}/4)= - cos(pi - {3pi}/4)=- cos(pi/4)= - 1/sqrt{2}cos(3π4)=−cos(π−3π4)=−cos(π4)=−1√2
sin({3pi}/4)=sin( pi - {3pi}/4) = sin(pi/4) = 1/sqrt{2}sin(3π4)=sin(π−3π4)=sin(π4)=1√2
tan({3pi}/4) = {sin({3pi}/4)}/{cos({3pi}/4)} = {1/sqrt{2}}/{-1/sqrt{2}}=-1tan(3π4)=sin(3π4)cos(3π4)=1√2−1√2=−1
sec({3pi}/4)=1/cos({3pi}/4) = - sqrt{2}sec(3π4)=1cos(3π4)=−√2
csc({3pi}/4)=1/sin({3pi}/4) = sqrt{2}csc(3π4)=1sin(3π4)=√2
cot({3pi}/4)=1/tan({3pi}/4) = -1cot(3π4)=1tan(3π4)=−1
