How do I factor and simplify these trigonometric expressions?
I don't get how to do these... I can factor the ones NOT involving stuff to the third power, but I don't know what to do when it IS to the third power! HELP! Can you please explain what you do, step-by-step? a) sin^3x + 27 b) 1 - 125tan^3x for a), I got (sin x + 3)^3 because I just took the 3rd root of everything... and then I wrote it to the third power, but the book says that that is wrong. for b) I did something similar and got (1 - 5tan x)^3, but again, that is wrong! What am I doing here?!! Better yet, what SHOULD I be doing? Thanks so much! I'll pick a best answer TODAY!!!!!!
Simplify trig expression 1+cscx / cosx+cotx?
(1 + cscx) / (cosx + cotx) = rewrite cscx and cotx in terms of sinx, cosx: [1 + (1/sinx)] / [cosx + (cosx/sinx)] = let sinx be the common denominator: [(sinx + 1)/sinx] / [(sinx cosx + cosx)/sinx] = [(sinx + 1)/sinx] [sinx / (sinx cosx + cosx)] = cancel sinx out: [(sinx + 1)/ (sinx cosx + cosx)] = factor out cosx from the denominator: [(sinx + 1)/ cosx (sinx + 1)] = cancel (sinx + 1) out: 1/ cosx = secx I hope it helps... Bye!
Factor the expression and use the fundamental identities to simplify (trig)?
1. cot^2x(1-cos^2x) (this one i don't know where to go from here) 2. sec^2x(tan^2x +1) = 1/cos^2x(cos^2x/sin^2x+1) (then the two cos^2x cancel) = 1/sin^2x +1 = cscx +1 ________ 1. (sinx+cosx) ^2 = sin^2x+cos^2x =1 2. cot^2x -cscx cotx + cscx cotx -csc^2x (then the two middle cscx cotx cancel) = cot^2x - csc^2x (i'm not sure if this one is finished) I hope the two I did finish help and maybe you can work on what I did for the other two
Can I simplify this trigonometric expression like this?
yes
Need help with simplifying trig equations?
1. sec²θ = tan²θ + 1 ((tanθ+1)(tanθ+1)−sec²θ) / tanθ = ((tan²θ + 2 tanθ + 1) − (tan²θ + 1)) / tanθ = 2 tanθ / tanθ = 2 2. Factor quadratic expression in cosθ the same way you would factor a quadratic expression in x: 5 cos²θ + 6 cosθ + 1 = 5 cos²θ + 5 cosθ + cosθ + 1 = 5 cosθ (cosθ + 1) + 1 (cosθ + 1) = (cosθ + 1) (5 cosθ + 1) Also cos²θ−1 factors as (cosθ−1)(cosθ+1) and not as cosθ(cosθ−1) (5 cos²θ + 6 cosθ + 1) / (cos²θ − 1) = (cosθ + 1) (5 cosθ + 1) / ((cosθ − 1) (cosθ + 1)) = (5 cosθ + 1) / (cosθ − 1) = 5 + 6/(cosθ − 1) 3. sec²θ = cot²θ + 1 (1 + cotθ) (1 − cotθ) − csc²θ = 1 − cot²θ − (cot²θ + 1) = −2 cot²θ