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

Prove the trigonometric identity $\cos\left(x+\frac{3\pi }{2}\right)=\sin\left(x\right)$

Step-by-step Solution

Go!
Symbolic 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 to the problem

true

Step-by-step Solution

How should I solve this problem?

  • Prove from LHS (left-hand side)
  • Prove from RHS (right-hand side)
  • Express everything into Sine and Cosine
  • Exact Differential Equation
  • Linear Differential Equation
  • Separable Differential Equation
  • Homogeneous Differential Equation
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Load more...
Can't find a method? Tell us so we can add it.
1

Starting from the left-hand side (LHS) of the identity

$\cos\left(x+\frac{3\pi }{2}\right)$
2

Multiply $3$ times $\pi $

$\cos\left(x+\frac{3\pi }{2}\right)$

Learn how to solve trigonometric identities problems step by step online.

$\cos\left(x+\frac{3\pi }{2}\right)$

Unlock unlimited step-by-step solutions and much more!

Create a free account and unlock a glimpse of this solution.

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity cos(x+(3*pi)/2)=sin(x). Starting from the left-hand side (LHS) of the identity. Multiply 3 times \pi . Divide 3\pi by 2. Using the cosine of a sum formula: \cos(\alpha\pm\beta)=\cos(\alpha)\cos(\beta)\mp\sin(\alpha)\sin(\beta), where angle \alpha equals x, and angle \beta equals \frac{3\pi}{2}.

Final answer to the problem

true

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

Help us improve with your feedback!

Function Plot

Plotting: $true$

Main Topic: Trigonometric Identities

In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables where both sides of the equality are defined.

Your Math & Physics Tutor. Powered by AI

Available 24/7, 365.

Unlimited 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:
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account