Posted by Kalen on Thursday, May 17, 2012 at 6:49pm.
write y=sinx-cosx in the form y=ksin (x+a), where the measure of a is in radians. answers: sqrt2sin (x+3pi/4), sqrt2sin (x+5pi/4), sqrt2sin (x+pi/4), or sqrt2sin (x+7pi/4) ...?
trig - Reiny, Thursday, May 17, 2012 at 7:03pm
ksin(x+a) = k(sinxcosa) + cosxsina)
= ksinxcosa + kcosxsina
ksinxcosa + kcosxsina = sinx - cosx , which must be an identity, so true for all x
let x =0
k(0)cosa + k(1)sina = 0-1
sina = 1/k
let x = 90°
k(1)(cosa) + k(0) = 1-0
cosa = 1/k
sina/cosa = (1/k) / (1/k)
tana = 1
a = 45° or π/4
then is sina = 1/k
√2/2 = 1/k
k = 2/√2 = √2
y = sinx - cosx
Answer This Question
More Related Questions
- trig - write y=sinx-cosx in the form y=ksin (x+a), where the measure of a is in ...
- trig - Solve the equation for cos theta-tan theta=0 for greater than or egual to...
- Math - Are these the solutions to sin2x sinx = cosx? pi/2, 3pi/2, 3pi/4, pi/4, ...
- Pre-Cal(Please check) - Approximate the equation's solutions in the interval (0,...
- Trig........ - I need to prove that the following is true. Thanks (cosx / 1-sinx...
- Precalculus/Trig - I can't seem to prove these trig identities and would really ...
- trigonometry - can i use factoring to simplify this trig identity? the problem ...
- Pre-Calc - Trigonometric Identities Prove: (tanx + secx -1)/(tanx - secx + 1)= ...
- Trigonometry Check - Simplify #3: [cosx-sin(90-x)sinx]/[cosx-cos(180-x)tanx] = [...
- maths - hey, i would really appreciate some help solving for x when: sin2x=cosx ...