Saturday

October 25, 2014

October 25, 2014

Posted by **lindsay** on Saturday, April 21, 2012 at 5:22pm.

- trigonometry -
**Reiny**, Saturday, April 21, 2012 at 5:56pmlet 3cosx - 2sinx = Rcos(x+a)

Rcos(x+a) = R(cosxcosa - sinxsina)

= Rcosxcosa - Rsinxsina

so we have the identity

Rcosxcosa - Rsinxsina = 3cosx-2sinx

this must be valid for any x

so let's pick x's that simplify this

let x = 0

then

Rcos0cosa - Rsin0sins = 3cos0 - 2sin0

Rcosa = 3

cosa = 3/R

let x = 90°

Rcos90cosa - Rsin90sina = 3cos90 - 2sin90

-Rsina = -2

sina = 2/R

but sin^2a + cos^2a = 1

4/R^2 + 9/R^2 = 1

R^2 = 13

R = √13

also : sina/cosa = (2/R) / (3/R) = 23

tana = 2/3

a = arctan (2/3) = 33.69°

thus 3cosx - 2sinx = √13cos(x + 33.69°)

check by taking any angle x

let x = 26°

LS =1.8196...

RS = √13 cos(5969) = 1.8196

........ how about that !!

**Answer this Question**

**Related Questions**

tigonometry - expres the following as sums and differences of sines or cosines ...

TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...

Mathematics - Trigonometric Identities - Let y represent theta Prove: 1 + 1/tan^...

trig - Reduce the following to the sine or cosine of one angle: (i) sin145*cos75...

Math - Calculus - The identity below is significant because it relates 3 ...

algebra - Can someone please help me do this problem? That would be great! ...

calculus - Differentiate. y= (cos x)^x u= cos x du= -sin x dx ln y = ln(cos x)^x...

Calc. - Differentiate. y= (cos x)^x u= cos x du= -sin x dx ln y = ln(cos x)^x ln...

pre-cal - Simplify the given expression........? (2sin2x)(cos6x) sin 2x and cos ...

math - Prove that for all real values of a, b, t (theta): (a * cos t + b * sin t...