Question

How do you find the exact value of $\cos 54$?

Answer 1

Hint: We explain the function $\cos 54$. We express the trigonometric function and find that it’s not in its normal angles where we can find the answer directly. We need to solve the equation in the calculator for a degree. We explain the process on how to solve the problem in the calculator.

Complete step by step answer:
First, we find the general solution of the equation $\cos 54$. The calculator settings usually remain in degree mode. There has to be a sign in the display board which is either ‘D’ or ‘R’ which tells us that it is either in degree or radian respectively.
Now if it’s in degrees then we need to first press the button which is for the \[\cos \] function. The main function in the board is \[\cos x\]. After pressing that button, we put the value for \[54\].
The rounded off value of $\cos 54$ in degree will be \[\cos 54=0.59\]. (approx.)
Now if we want to find it in radian, we can convert it into radian using the relation where 1 degree is equal to $\dfrac{\pi }{180}$ radian. This gives ${{54}^{\circ }}$ is equal to $\dfrac{\pi }{180}\times 54$ radian. We evaluate the value in radians.
we press the key with ‘mode’ written over it. The first thing that comes on screen is the choice of radian, degree and many others. We click the required numeric value mentioned in the screen to convert into radian mode and do the same process to find the radian value which will be \[\cos \left( \dfrac{\pi }{180}\times 54 \right)=0.59\]. (approx.)

Note: The domain for the degree value in the calculator and also in the primary solution for inverse of ratio sin is $-\dfrac{\pi }{2}\le x\le \dfrac{\pi }{2}$. Instead of using relation to get the radian value we can also directly use the calculator to find the radian value by just changing the setting from degree to radian.