Circular functions

[kamil9876]

2.)

(1)

Because in second quadrant
(2)


(3)

just sub (2) and (3) back into (1)

[Damo17]

Couple of Q's guys...

1. equals:
A.
B.
C.
D.
E.


Need to see workings for em

thanks !

1.)   

[dcc]

If that was a multiple choice question on a VCE MM exam (non-CAS), what I would use to do is input each option into the Y menu, and then graph the functions.  If the two functions overlapped everywhere (except perhaps some naughty discontinuities), then they were obviously equal.

Only do this if you are quick at using your calculator though.  I rationalised that it was quicker for me to type these in then do the algebra, but you might not be the same.  Also don't check 'silly' answers which are obviously not correct, as that is a waste of time.

[TrueTears]

If that was a multiple choice question on a VCE MM exam (non-CAS), what I would use to do is input each option into the Y menu, and then graph the functions.  If the two functions overlapped everywhere (except perhaps some naughty discontinuities), then they were obviously equal.

Only do this if you are quick at using your calculator though.  I rationalised that it was quicker for me to type these in then do the algebra, but you might not be the same.  Also don't check 'silly' answers which are obviously not correct, as that is a waste of time.

Yeah true, I do another thing, if you can not figure out the answer just type in a random value for x and test each x to see if you get the same answer. [if non calc just sub in an exact value]

[dcc]

I wouldn't use any method similar to this without a calculator.  Exact values will (with an infinitely larger probability) overlap more often (i.e. cos/sin at pi/4). 

[TrueTears]

Couple of Q's guys...

1. equals:
A.
B.
C.
D.
E.


Need to see workings for em

thanks !

1.)   

That question was on my spesh test once. Quite fun.

[d0minicz]

ahhhhh cheers guys

[QuantumJG]

Neeed help on a couple of questions

a)

a) [tan^2(x) + 1]/tan^2(x) = 1 + cot^2(x) = cosec^2(x)

b)

(sin^2(x) + cos^2(x))(sin^2(x) - cos^2(x)) = (sin^2(x) - cos^2(x)) = (1 - cos^2(x) - cos^2(x)) = 1 - 2cos^2(x) = -cos(2x)

AND


If ,    , find:

a)

b)

c)


thank you

x = arccot(3)

a) cosecx = cosec(arccot(3)), where, cosec(x)<0

cosec(arccot(3)) = -sqrt(1 + cot^2(arccot(3)) = -sqrt(10)

b) sin(x) = 1/cosec(x) = -1/sqrt(10) = sqrt(10)/10

c) sec(x) = -sqrt(1 + tan^2(arccot3)), since, sec(x)<0

= -sqrt(1 + [1/(cot^2(arccot3))])

= -sqrt(10/9)

= -sqrt(10)/3

[TrueTears]

Eh won't those answered ages ago?

EDIT*  There is never a good reason to quote the preceding post in its entirety.  Especially if its large!