# Step-by-step Solution

## Solve the trigonometric equation $\sin\left(x\right)-\left(\frac{\sqrt{2}}{2}\right)=0$

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### Videos

$x=\frac{1}{4}\pi+2\pi n,\:x=\frac{3}{4}\pi+2\pi n$

## Step-by-step Solution

Problem to solve:

$sin\left(x\right)-\frac{\sqrt{2}}{2}=0$
1

We need to isolate the dependent variable $x$, we can do that by subtracting $-\frac{\sqrt{2}}{2}$ from both sides of the equation

$\sin\left(x\right)=\frac{\sqrt{2}}{2}$
2

The angles where the function $\sin\left(x\right)$ is $\frac{\sqrt{2}}{2}$ are

$x=45^{\circ}+360^{\circ}n,\:x=135^{\circ}+360^{\circ}n$
3

The angles expressed in radians in the same order are equal to

$x=\frac{1}{4}\pi+2\pi n,\:x=\frac{3}{4}\pi+2\pi n$

$x=\frac{1}{4}\pi+2\pi n,\:x=\frac{3}{4}\pi+2\pi n$
SnapXam A2

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1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

$sin\left(x\right)-\frac{\sqrt{2}}{2}=0$