Posted by T.Gracken on October 21, 2002 at 18:12:18:
In Reply to: Pre-calc posted by Jacquie on October 21, 2002 at 17:50:43:
: im confused as to what this means:
: If cot= 3pi/4 find sin x for x between pi and 3pi/2
: does this mean that my answer has to be in the second quadrant if so how exactly do i do this?
: what formula do i use to verify tanxcscx=secx?
it means nothing.
do you mean if cot(x) = 3pi/4 determine sin(x) for x between pi and 3pi/2?
if so, one way is use triangles. If not, rewrite the problem carefully and give us more info as to what you have tried (unit circle approach, wrapping function, triangle definitions, etc)
as for verify... you don't use a formula, you use "fundamental" identities...
that is,
since tan(x)= sin(x)/cos(x) {quotient identity}
and csc(x) = 1/sin(x) {reciprocal identity},
you can rewrite tan(x)csc(x) as sin(x)/cos(x)*1/sin(x) using the principal of substitution.
cancel common factors in the fraction {the sin(x)'s} to be left with 1/cos(x), and this is equal to sec(x) {another reciprocal identity}