trig inequality (1 Viewer)

[kractus]

how do u do this?
I got -2 < tanx < 3 but idk how to go from there given the domain 0<x<360
like do i just arctan everything and yeh or what else do i do

if i arctan i got 0<x<71deg 34'. I'm like super unsure about it tho

 

[Drongoski]

 

[Average Boreduser]

View attachment 38152
how do u do this?
I got -2 < tanx < 3 but idk how to go from there given the domain 0<x<360
like do i just arctan everything and yeh or what else do i do

if i arctan i got 0<x<71deg 34'. I'm like super unsure about it tho

You factorise brother. Take 6 to the other side, maybe let tank=u or smn initially, then solve for tanx

 

[kractus]

also this q (its a proof)

 

[kractus]

ye, where do u go from there tho to isolate x or do u keep it like that?

 

[Average Boreduser]

ye, where do u go from there tho to isolate x or do u keep it like that?

Keep it like that

 

[Average Boreduser]

View attachment 38153
also this q (its a proof)

I’m in the car so I can’t be really that accurate, but from the looks of it, most likely you take reciprocal of cosec and sinx/cosx of tan and try making into form of the rhs

 

[Lith_30]

View attachment 38153
also this q (its a proof)

 

[cossine]

ye, where do u go from there tho to isolate x or do u keep it like that?

You want make use of the following theorems:

f^-1 (f(x)) = x
f(f^-1(x)) = x

# The theorem are fairly easy to prove if (x, y) is point of "f" than (y, x) is a point of f^-1 // By definition of inverse function
# Similarly if (x, y) is point of "f^-1" than (y, x) is a point of f

You will also need to consider the unit circle definition of tan(theta) i.e. tan(theta) = y/x as well as ASTC.

 

[kractus]

oh bruh thats such an easy proof i just think of compound angle straight away cause like tanpi/4 is just 1 its so tempting lol

 

[Lith_30]

oh bruh thats such an easy proof i just think of compound angle straight away cause like tanpi/4 is just 1 its so tempting lol

yeah but then you have to find out

 

[kractus]

yeah but then you have to find out

wait i thought it was pi/4 I'm blind ahhaha

 

[gazzaboy]

ye, where do u go from there tho to isolate x or do u keep it like that?

You want to isolate the x. But because it's an inequality, it's a little tricky because you can't just use the inverse tangent function without accounting for what your domain is. Remember that the inverse tangent function takes the range (-pi/2,pi/2)

One way to do it is to draw a graph. So you want to graph y = tan(x), y=3 and y=-2, and then find the parts of the tangent graph that are 'between the two lines'. Depending on your domain, you might get multiple segments.

For example, if your domain is , then your answer is , and