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

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##  Final answer to the problem

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

How should I solve this problem?

• Choose an option
• Express in terms of sine and cosine
• Simplify
• Simplify into a single function
• Express in terms of Sine
• Express in terms of Cosine
• Express in terms of Tangent
• Express in terms of Cotangent
• Express in terms of Secant
• Express in terms of Cosecant
Can't find a method? Tell us so we can add it.
1

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

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

Multiplying the fraction by $-1$

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

The angles where the function $\sin\left(x\right)$ is $0$ 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

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

##  Final answer to the problem

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

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SnapXam A2

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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

###  Main Topic: Trigonometric Equations

A trigonometric equation is an equation in which one or more trigonometric ratios appear.