inverse trig question (1 Viewer)

[Grey Council]

How would I prove that:
arcsinx = arccos (1 - x2)1/2
?

and is
arccosx = arcsin (1 - x2)1/2
similar?

another question (i only want an explanation on what this question means, lol, not how to do it, i'll have a shot first)
Given f(x) = sin(2x-3) for all x, write down the range of f. (got this bit). Show that a restriction of f, namely F, defined on [1,2], has an inverse F^-1, and sketch the graph.
?!? what does it mean, defined on [1,2]?!?

hrm

 

[Affinity]

1.) use derivatives, remember d/dx arccos(x) = - 1/sqrt(1-x^2)

or you could use pythagoras' theorem

2.) that means we only define F(x) for x in [1,2] F(3) for example is undefined, intuitively, imagine erasing the graph of f(x) for all x>2 and all x<1

 

[Affinity]

by the way, equality only hold for positive x's

 

[Grey Council]

haven't done differentiation of inverse functions.
so will use pythagoras. somehow. ^_^

and thanks.

 

[CM_Tutor]

Originally posted by Grey Council
How would I prove that:
arcsinx = arccos (1 - x2)1/2
?

and is
arccosx = arcsin (1 - x2)1/2
similar?

The easiest way is to show that sin(LHS) = sin(RHS), or cos(LHS) = cos(RHS), and then explain why LHS and RHS must be in the same quadrant. It then follows that LHS = RHS - and yes, the second one is extremely similar

 

[Grey Council]

*hits himself on head*
damn, i've just been taking the sin of both sides for like the lsat 10 questions.

and i didn't think of doing it to this question.

man, i'm so stoopid sometimes.