Question

Select the functions that have a value of -1. sin180° cos180° tan180° csc180° sec180° cot180°

Answer 1

We have to break each degree in terms of 90

A) $sin180^\circ=sin(90\times2+0)$

Which is in third quadrant, therefore sine is negative hence

$sin(90\times2+0)= -sin0 ^\circ = 0$

B) $cos180^\circ =cos(90\times2+0)$

Which is in third quadrant, therefore cosine is negative hence

$cos(90\times2+0)= -cos0^\circ = -1$

C) $tan180^\circ=tan(90\times2+0)$

Which is in third quadrant, therefore tangent is positive hence

$tan(90\times2+0)= tan0^\circ = 0$

D) $csc180^\circ=csc(90\times2+0)$

Which is in third quadrant, therefore cosec is negative hence

$cosec(90\times2+0)= -csc0^\circ =$not defined

E)$sec180^\circ=sec(90\times2+0)$

Which is in third quadrant, therefore secant is negative hence

$sec(90\times2+0)= -sec0^\circ = -1$

F) $cot180^\circ=cot(90\times2+0)$

Which is in third quadrant, therefore tangent is positive hence

$cot(90\times2+0)= cot0^\circ =$ not defined

Hence only $cos 180^\circ$ and

$sec180^\circ$ have value -1

Hope this will help