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# Solve the trigonometric equation $4\sin\left(x\right)^2-3=0$

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##  Final answer to the problem

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

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• 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
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1

We need to isolate the dependent variable $x$, we can do that by simultaneously subtracting $-3$ from both sides of the equation

$4\sin\left(x\right)^2=3$

Learn how to solve differential calculus problems step by step online.

$4\sin\left(x\right)^2=3$

Learn how to solve differential calculus problems step by step online. Solve the trigonometric equation 4sin(x)^2-3=0. We need to isolate the dependent variable x, we can do that by simultaneously subtracting -3 from both sides of the equation. Divide both sides of the equation by 4. Removing the variable's exponent. Calculate the power \sqrt{\frac{3}{4}}.

##  Final answer to the problem

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

##  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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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: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.