👉 Try now NerdPal! Our new math app on iOS and Android

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

Step-by-step Solution

Go!
Math mode
Text mode
Go!
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

Final Answer

$x=\frac{1}{4}\pi+2\pi n,\:x=\frac{3}{4}\pi+2\pi n\:,\:\:n\in\Z$
Got another answer? Verify it here!

Step-by-step Solution

Specify the solving method

1

Calculate the square root of $2$

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

Multiply $-1$ times $\sqrt{2}$

$\sin\left(x\right)-\frac{\sqrt{2}}{2}=0$
3

Divide $-\sqrt{2}$ by $2$

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

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

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

$x+0=x$, where $x$ is any expression

$\sin\left(x\right)=\frac{\sqrt{2}}{2}$
4

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

$\sin\left(x\right)=\frac{\sqrt{2}}{2}$
5

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

$x=45^{\circ}+360^{\circ}n,\:x=135^{\circ}+360^{\circ}n$
6

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

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

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

Verify if true (using algebra)Verify if true (using arithmetic)

Give us your feedback!

Function Plot

Plotting: $\sin\left(x\right)+\frac{-\sqrt{2}}{2}$

SnapXam A2
Answer Assistant

beta
Got a different answer? Verify it!

Go!
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

How to improve your answer:

Main Topic: Trigonometric Equations

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

Related Topics

Your Math & Physics Tutor. Powered by AI

Available 24/7, 365.

Complete step-by-step math solutions. No ads.

Includes multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android apps as well.

20% discount on online tutoring.

Choose your Subscription plan:
Have a promo code?
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account