Step-by-step Solution

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

Go!
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sinh
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asinh
acosh
atanh
acoth
asech
acsch

Final Answer

$x=\frac{1}{4}\pi+2\pi n,\:x=\frac{3}{4}\pi+2\pi n$
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Step-by-step Solution

Problem to solve:

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

Simplifying

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

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

$\sin\left(x\right)=\frac{\sqrt{2}}{2}$
3

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

$x=45^{\circ}+360^{\circ}n,\:x=135^{\circ}+360^{\circ}n$
4

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

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

Final Answer

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

Tips on how to improve your answer:

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

Time to solve it:

~ 0.31 s

Related topics:

Trigonometric Equations