using the formula cos A =+- root over( 1+cos 2A)/2 find the value of 67 1/2 degree
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Answer:
formula doesn't tell us whether
sin
67.5
∘
is positive or negative, but, since it is an acute angle we know that the sine is positive. (Be careful of the difference between "sign" and "sine").
We also need
cos
135
∘
. (That is the special angle that is
45
∘
in Quadrant II.)
cos
135
∘
=
−
√
2
2
.
Now use the formula ans simplify:
sin
67.5
∘
=
sin
(
1
2
(
135
∘
)
)
=
√
1
−
cos
135
∘
2
=
⎷
1
−
(
−
√
2
2
)
2
=
⎷
1
+
√
2
2
2
=
√
2
+
√
2
4
=
√
2
+
√
2
2
sin
67.5
∘
=
√
2
+
√
2
2
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