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Solve the trigonometric equation $\sin\left(x\right)=-\frac{1}{2}$

Step-by-step Solution

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Final Answer

$x=\frac{7}{6}\pi+2\pi n,\:x=\frac{11}{6}\pi+2\pi n\:,\:\:n\in\Z$
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Step-by-step Solution

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1

The angles where the function $\sin\left(x\right)$ is $-\frac{1}{2}$ are

$x=210^{\circ}+360^{\circ}n,\:x=330^{\circ}+360^{\circ}n$
2

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

$x=\frac{7}{6}\pi+2\pi n,\:x=\frac{11}{6}\pi+2\pi n\:,\:\:n\in\Z$

Final Answer

$x=\frac{7}{6}\pi+2\pi n,\:x=\frac{11}{6}\pi+2\pi n\:,\:\:n\in\Z$

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Function Plot

Plotting: $\sin\left(x\right)+\frac{1}{2}$

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7
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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.

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