Doing this review for calc, I'm a little rusty on the trig :(
Simplify using an appropiate right triangle
Sec[tan x]
2007-01-21 17:29:44 · 3 answers · asked by Dr. Daniel 2 in Science & Mathematics ➔ Mathematics
?? Should this be sec (arctan x), perhaps? It doesn't make much sense the way it is.
Assuming you want sec (arctan x), take a right triangle with one angle θ. We want to let θ = arctan x, i.e. tan θ = x. So let x be the length of the side opposite θ and let the length of the adjacent side be 1. Then the hypotenuse is √(x^2 + 1).
So sec (arctan x) = sec θ = 1 / cos θ = hyp / adj = √(x^2 + 1) / 1 = √(x^2 + 1).
2007-01-21 17:36:27 · answer #1 · answered by Scarlet Manuka 7 · 1⤊ 0⤋
This doesn't make sense as it stands. Shouldn't it be
sec[tan^(-1) x] or sec[arctan x]?
If tan t = x, (x being the length of the "leg" opposite the angle 't', and 1 being the length of the other "leg" next to the angle), then the length of the hypoteneuse = sqrt [1 + x^2], or [1 + x^2]^(1/2).
Then what you want is sec t (= 1/[cos t]) = sqrt [1 + x^2], or [1 + x^2]^(1/2). QED.
Live long and prosper --- and hats off to Scarlet Manuka, who got in before me, I now see.
2007-01-21 17:36:46 · answer #2 · answered by Dr Spock 6 · 0⤊ 0⤋
a million) factor out sin^a million/2 from unique equation sin^a million/2(cos x - sin^(4/2)xcosx 2)sin^(4/2)x = sin^2 x by using simplificaiton 3) sin^2 x = a million - cos^2 x by using pythagorean identities 4) rewrite... and simplify... it's going to all artwork out simply by fact the splendid facet
2016-12-12 17:19:49 · answer #3 · answered by zagel 4 · 0⤊ 0⤋