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Solve the equation $z=\arctan\left(2x+y\right)$

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Solution

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Final Answer

$y=\tan\left(z\right)-2x$
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Step-by-step Solution

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Rearrange the equation

$\arctan\left(2x+y\right)=z$

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$\arctan\left(2x+y\right)=z$

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Learn how to solve trigonometric equations problems step by step online. Solve the equation z=arctan(2x+y). Rearrange the equation. Take the inverse of \arctan\left(2x+y\right) on both sides. Since arctan is the inverse function of tangent, the tangent of arctangent of 2x+y is equal to 2x+y. We need to isolate the dependent variable , we can do that by simultaneously subtracting 2x from both sides of the equation.

Final Answer

$y=\tan\left(z\right)-2x$

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

Solve for zSolve for xSolve for yFind the discriminantSimplifyFactorFactor by completing the squareFind the integralFind the derivativeFind z=arctan(2x+y) using the definitionSolve by quadratic formula (general formula)Find the rootsFind break even pointsFind the discriminantFind the derivativeSolve by implicit differentiationSolve for y'Find dy/dxDerivative

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Function Plot

Plotting: $z-\arctan\left(2x+y\right)$

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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
D□x
∫
∫◻
|◻|
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

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Main Topic: Trigonometric Equations

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

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