YEAR 12 ADVANCED TRIGONOMETRIC EQUATIONS (1 Viewer)

[ebony_17]

Graph y = -cos(x) + 3 and y = x-1 for [0 2pi]
then solve
-cos(x) + 3 = x-1
and -cos(x) + 3 = 2
The solving algebraically is where I'm getting confused.

 

[cossine]

Graph y = -cos(x) + 3 and y = x-1 for [0 2pi]
then solve
-cos(x) + 3 = x-1
and -cos(x) + 3 = 2
The solving algebraically is where I'm getting confused.View attachment 29536

-cos(x) +3 = x - 1

=> -cos(x) - x + 4 = 0

I don't think is there an algebraic way. to solve this.

I would try Newton's method but that will only give you an approximate solution.

 

[black.mamba]

There is no way to solve this algebraically (the equation is a transcendental equation).

 

[Greninja340]

Graph y = -cos(x) + 3 and y = x-1 for [0 2pi]
then solve
-cos(x) + 3 = x-1
and -cos(x) + 3 = 2
The solving algebraically is where I'm getting confused.View attachment 29536

Usually when they give questions like that they are only asking for the amount of solutions

 

[black.mamba]

im guessing the question is just asking for answers to a few decimal places, which can be found on desmos as the x-coordinates of the intersection points

 

[CM_Tutor]

Graph y = -cos(x) + 3 and y = x-1 for [0 2pi]
then solve
-cos(x) + 3 = x-1
and -cos(x) + 3 = 2
The solving algebraically is where I'm getting confused.

The second equation here,



is solvable, though