How can I solve this equation?

Question

How can I solve for a?

The equation is 38.28825 - 24.375a = 22.25Cos[a]


Can you please tell me can kind of equation is this, polynomial, trig...? and if if posible how to solve this equation.

Thanks

Thanks, I was going to solve it using Matematica, but I don't know what command to write, it does not do with "Solve"

Answer 1

This is a non-linear equation, and there isn't any real analytical way to solve it. You can't really isolate the "a" when you have that cos(a) term in the equation too. In these cases, you usually have to resort to using an approximation method, for example something like Newton's method where you keep plugging in values recursively.

However, it might help to note a couple of things. f(a) = 38.28825 - 24.375a is a line with a negative slope and y-intercept of 38.28825 and x-intercept of about 1.5708 which is very close to pi/2, though a tiny bit more. The right-hand side is just a cosine wave with an amplitude of 22.25, so one of the intersections is going to be somewhere in the vicinity of a = pi/2. In fact, it might be the only one, depending on if the line clears most of the wave.

Answer 2

i dont know wat kind of equation this is ... it seems to be a mixed type of polynomial and trig. I know one method to solve such equations using calculator.

press 1 and press = to get 1 as answer

now type (38.28824 - 22.25 cos (Ans))/24.375
keep pressing = until u get a value that doesnt change much while pressing =

that value wud be an approx. solution to this equation.

I dont hv a calculator rt now or else i cud hv tried it.

If the above method doesnt work out, try this too:
cos-inverse ( (38.28825 - 24.375*Ans)/22.25)
one of these is sure to give u the answer

Answer 3

Because it contains Cos[a], it is a trigonometrical equation.
Effectually you have two unknowns in one equation, so more information is needed to calculate the value of 'a'.

Answer 4

This is a trigonometrical function of first order, involving 'cosine function' and angle 'a' in radian measure. Since, 'a' is in radian measure, the value of 'a' will be approximate one as value of radian itself is appx. only .
There will be only one distinct solution to above equation .

Answer 5

This is a transcendental. You can't solve it numerically, but you can solve it numerically.
38.28825 - 24.375a = 22.25Cos[a]
24.375a = 38.28825 - 22.25Cos[a]
a = 1.5708 - 0.91282Cos[a]
Set this recursive up in a column on Excel to get
1.57083846
1.57083846
1.57083846
1.57083846
1.57083846
1.57083846
after a number of estimations. (It doesn't converge very rapidly)