conclusion of trigonometric ratios of 30 degree and 60 degree
Answers
Answer:
Angles
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We can determine the trigonometric ratios for the following five angles based on our existing knowledge of pure geometry:
0
∘
,
30
∘
,
45
∘
,
60
∘
a
n
d
90
∘
. Let us see how:
Trigonometric Ratios of
0
∘
a
n
d
90
∘
Consider a
Δ
A
B
C
which is right-angled at
B
, such that
∠
A
is very small:
T-ratios of 0 and 90 degrees
✍Note: As
∠
A
is close to
0
∘
,
∠
C
is close to
90
∘
.
Now,
sin
A
=
B
C
A
C
will be very small (close to 0), because
B
C
is very small.
cos
A
=
A
B
A
C
will be almost equal to 1, because the base
A
B
is almost equal to the hypotenuse
A
C
.
Visualize what would happen if
∠
A
was made smaller and smaller until it became
0
∘
.
In this scenario,
sin
A
would become exactly 0.
cos
A
would become exactly 1.
Thus, we conclude that
sin
0
∘
=
0
,
cos
0
∘
=
1
If we analyze the sine and cosine of
∠
C
in the same situation, we can conclude that
sin
90
∘
=
1
,
cos
90
∘
=
0
We summarize these findings below:
sin
0
∘
=
0
,
sin
90
∘
=
1
cos
0
∘
=
1
,
cos
90
∘
=
0