Respuesta :
We have to break each degree in terms of 90
A) [tex]sin180^\circ=sin(90\times2+0)[/tex]
Which is in third quadrant, therefore sine is negative hence
[tex]sin(90\times2+0)= -sin0 ^\circ = 0[/tex]
B) [tex]cos180^\circ =cos(90\times2+0)[/tex]
Which is in third quadrant, therefore cosine is negative hence
[tex]cos(90\times2+0)= -cos0^\circ = -1 [/tex]
C) [tex] tan180^\circ=tan(90\times2+0)[/tex]
Which is in third quadrant, therefore tangent is positive hence
[tex]tan(90\times2+0)= tan0^\circ = 0[/tex]
D) [tex]csc180^\circ=csc(90\times2+0)[/tex]
Which is in third quadrant, therefore cosec is negative hence
[tex]cosec(90\times2+0)= -csc0^\circ =[/tex]not defined
E)[tex]sec180^\circ=sec(90\times2+0)[/tex]
Which is in third quadrant, therefore secant is negative hence
[tex]sec(90\times2+0)= -sec0^\circ = -1 [/tex]
F) [tex] cot180^\circ=cot(90\times2+0)[/tex]
Which is in third quadrant, therefore tangent is positive hence
[tex]cot(90\times2+0)= cot0^\circ = [/tex] not defined
Hence only [tex] cos 180^\circ [/tex] and
[tex] sec180^\circ [/tex] have value -1
Hope this will help
