Answer: sin(90
∘
)
=
1
xx
sin
(
180
∘
)
=
0
cos
(
90
∘
)
=
0
cos
(
180
∘
)
=
−
1
tan
(
90
∘
)
is undefined
tan
(
180
∘
)
=
0
Step-by-step explanation: For the unit circle we have the situations pictured below;
90
∘
and
180
∘
are limits as the hypotenuse approaches the (positive) vertical axis and the (negative) horizontal axis respectively.
enter image source here
By definition:
XXX
sin
=
opposite
hypotenuse
XXX
cos
=
adjacent
hypotenuse
XXX
tan
=
opposite
adjacent
As limits we can see that
XXX
sin
(
90
∘
)
=
1
1
=
1
xx
sin
(
180
∘
)
=
0
−
1
=
0
cos
(
90
∘
)
=
0
1
=
0
cos
(
180
∘
)
=
−
1
1
=
−
1
tan
(
90
∘
)
=
1
0
: undefined
tan
(
180
∘
)
=
0
−
1
=
0
