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

then

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

ksina= 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

then

y = sinx - cosx

= √2sin(x+π/4)

## Answer this Question

## 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...
- 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 ...
- maths - hey, i would really appreciate some help solving for x when: sin2x=cosx ...
- 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] = [...
- trig - Sketch a unit circle and label the terminal points corresponding to t= pi...

More Related Questions