2 Answers

Giannis · Answer 1 · 2019-07-26T01:00:53+0000

We have to break each degree in terms of 90

A)
$sin180^\circ=sin(90*2+0)$

Which is in third quadrant, therefore sine is negative hence

$sin(90*2+0)= -sin0 ^\circ = 0$

B)
$cos180^\circ =cos(90*2+0)$

Which is in third quadrant, therefore cosine is negative hence

$cos(90*2+0)= -cos0^\circ = -1$

C)
$tan180^\circ=tan(90*2+0)$

Which is in third quadrant, therefore tangent is positive hence

$tan(90*2+0)= tan0^\circ = 0$

D)
$csc180^\circ=csc(90*2+0)$

Which is in third quadrant, therefore cosec is negative hence

$cosec(90*2+0)= -csc0^\circ =$ not defined

E)
$sec180^\circ=sec(90*2+0)$

Which is in third quadrant, therefore secant is negative hence

$sec(90*2+0)= -sec0^\circ = -1$

F)
$cot180^\circ=cot(90*2+0)$

Which is in third quadrant, therefore tangent is positive hence

$cot(90*2+0)= cot0^\circ =$ not defined

Hence only
$cos 180^\circ$ and

$sec180^\circ$ have value -1

Hope this will help

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