Question

θ lies in Quadrant III. sec(θ)=-25/7 how do you find the values of all six trigonometric functions?

Answer 1

sec (x)=1/cos(x) so in your case cos(x)=-7/25 sin(x)=sqrt(1-cos^2(x))=26/25 tanx=sin(x)/cos(x)=-26/7 cotan(x)=1/tan(x)=-7/26 cosec(x)=1/sin(x)=25/26

Answer 2

sorry my mistake, if it lies in 3. quadrant then sin(x)=-26/25 (sin is negative in 3. quadrant) so just change signs for tan, cotan and cosec

Answer 3

so cosec=-25/26?

Answer 4

yes

Answer 5

thank you !

Answer 6

you're welcome