/4
Evaluate :
sin x + cos x
-dx
16 +9sin 2x
.
0
Answers
Answer:
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How do you solve
cos
x
+
sin
x
tan
x
=
2
over the interval 0 to 2pi?
Trigonometry Trigonometric Identities and Equations Solving Trigonometric Equations
2 Answers
Ahmemaru
May 9, 2018
x
=
π
3
x
=
5
π
3
Explanation:
cos
x
+
sin
x
tan
x
=
2
tan
x
=
sin
x
cos
x
cos
x
+
sin
x
(
sin
x
cos
x
)
=
2
cos
x
+
sin
2
x
cos
x
=
2
cos
2
x
cos
x
+
sin
2
x
cos
x
=
2
cos
2
x
+
sin
2
x
cos
x
=
2
cos
2
x
+
sin
2
x
=
1
the phythagrean identity
1
cos
x
=
2
multiply both sides by
cos
x
1
=
2
cos
x
divide both sides by
2
1
2
=
cos
x
cos
x
=
1
2
from the unit circle
cos
(
π
3
)
equals
1
2
so
x
=
π
3
and we know that
cos
is positive in the first and fourth quadrant so find an angle in the fourth quadrant that
π
3
is the reference angle of it
so
2
π
−
π
3
=
5
π
3
so
x
=
π
3
,
5
π
3
Answer link
Dean R.
May 9, 2018
x
=
π
3
or
5
π
3
Explanation:
The way I'm checking the other answer is writing my own.
cos
x
+
sin
x
tan
x
=
2
cos
x
+
sin
x
(
sin
x
cos
x
)
=
2
cos
2
x
+
sin
2
x
=
2
cos
x
1
=
2
cos
x
cos
x
=
1
2
There's the cliche triangle, you knew it was coming.
In the range,
x
=
π
3
or
5
π
3
Check:
cos
(
5
π
3
)
+
sin
(
5
π
3
)
tan
(
5
π
3
)
=
1
2
+
−
√
3
2
⋅
−
√
3
/
2
1
/
2
=
1
2
+
3
2
=
2
√
Answer link
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