trig help (1 Viewer)

[stressedadfff]

does anyone know how to find multiple solutions for such a equation? thank youu

 

[cossine]

does anyone know how to find multiple solutions for such a equation? thank youu
View attachment 33719

Is this an advance question?

I believe microsoft calculator can solve these types of question

The general solution for:

cos(theta) = a

is

2*n*pi +/- alpha (1)

______________________
sin theta = a

is

theta = n*pi +(-1)^n * alpha (2)

_______________________
tan(theta) = a

is

theta = n*pi + alpha (3)

____________________________

Of course you are not going to be able to apply theorem (1)/(2)/(3) in these types of questions because of the coefficent of t is 2pi/3 not 1.

So let u = 2pi/3 * t. With this substitution you can now apply the theorem as the coefficent is now 1 which is coefficent of theta.

So you have

u = n*pi +(-1)^n * alpha # note alpha = sin^-1(a)

2pi/3 * t = n*pi +(-1)^n * alpha # make t the subject and your done.


Note: To save time in a exam you don't need to actually substitute u.

 

[stressedadfff]

thank youse!!