trig identities help

quickquestion805

Find without using a calculator, the value of:
sinx and cosx, given that tanx=5/12 and x is acute

Reply 1

quickquestion805

is there any way of doing it other than this method? not too fond of it.

Reply 2

mqb2766

Original post by quickquestion805

is there any way of doing it other than this method? not too fond of it.

Thats about the simplest/most obvious way. Why are you not fond of it?

(edited 10 months ago)

Reply 3

quickquestion805

Original post by mqb2766

Thats about the simplest/most obvious way. Why are you not fond of it?

For questions that give us sinx and cosx, I prefer to use the sin2x+cos2x=1 and sinx/cosx=tanx identities to find the solution. So, I'd prefer to use the same method if possible.

Reply 4

mqb2766

Original post by quickquestion805

For questions that give us sinx and cosx, I prefer to use the sin2x+cos2x=1 and sinx/cosx=tanx identities to find the solution. So, I'd prefer to use the same method if possible.

You could use the pythagorean identities
1 + tan^2(x) = sec^2(x)
to get cos(x), then
sin^2(x) + cos^2(x) = 1
or
tan(x)=sin(x)/cos(x)
to get sin(x) but its more complex and really youre just doing pythagoras (twice).

The mark scheme method is useful for deriving idenites for arcsin etc and similar stuff comes up in mechanics when you resolve forces etc, so if youre not happy with it, maybe its time to become happier?