Question

Solve for theta Cos 3 theta/2=1/2​

Answer 1

Answer:

theta = 20 degrees

Step-by-step explanation:

we know cos 60= 1/2

therefore cos 3 theta = cos 60

and theta = 60/3

                = 20 degrees

no need to follow any one for answers

Answer 2

Answer:

The solution for $cos\frac{3\theta}{2}=\frac{1}{2}$ is $\theta=\frac{2\pi}{3}(2n\pm\frac{1}{3}) , n\epsilon I$

Step-by-step explanation:

Firstly, $cos \frac{3\theta}{2}$ is given to be equal to $\frac{1}{2}$

We know that :

$cos \frac{\pi}{3} =\frac{1}{2} \\\\cos \frac{3\theta}{2}= cos \frac{\pi}{3}$

Now, we know that : if $cos \theta=cos\alpha$

$\theta=2n\pi\pm\alpha$

$\frac{3\theta}{2}=2n\pi\pm\frac{\pi}{3}$, $n\epsilon I$   -- Let this be (i)

Multiplying (i) with $2$ :

$3\theta=4n\pi\pm\frac{2\pi}{3}$

$\theta=\frac{4n\pi}{3}\pm\frac{2\pi}{9}$

Taking the common term outside :

$\theta=\frac{2\pi}{3}(2n\pm\frac{1}{3}) , n\epsilon I$

What is an equation's general solution?

The general solution often contains arbitrary constants (in the case of an ODE) or arbitrary functions, and it encompasses all feasible solutions (in the case of a PDE.)

A specific solution is one that contains no arbitrary constants or functions.

Trigonometric functions:

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths.

They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.