Question

If sin θ=−12/13 with 3π/2<θ<2π , find each of the following: (a) sin(θ−5π/4) (b) cos(θ−11π/6) c) tan(θ+5π/4) If sin θ=−12/13 with 3π/2<θ<2π , find each of the following: (a) sin(θ−5π/4) (b) cos(θ−11π/6) c) tan(θ+5π/4) @Mathematics

Answer 1

lord we can do this but what a pain. first of all we need
\[\cos(\theta)\]

Answer 2

since you are in quadrant III it is positive, and by pythagoras is it
\[\cos(\theta)=\frac{5}{13}\]

Answer 3

it shuld be negative in quadrant III

Answer 4

then for
\[\sin(\theta-\frac{5\pi}{4})\] use the "subtraction angle formula"
\[\sin(\alpha -\beta)=\sin(\alpha)\cos(\beta) -\sin(\beta)\cos(\alpha)\] with
\[\sin(\alpha)=-\frac{12}{13}, \cos(\alpha)=\frac{5}{13}, \sin(\beta)=\sin(\frac{5\pi}{4})=-\frac{\sqrt{2}}{2},\cos(\frac{5\pi}{4})=-\frac{\sqrt{2}}{2}\]\]

Answer 5

my mistake you are in quadrant IV

Answer 6

plug in the numbers get out the answer

Answer 7

hw is it quadrant iv?