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# TRIGONOMETRIC EQUATION HELP!!

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441
7

(square root 5) cos (2x+0.464) = 1

0<=x<pi

Supposed to give 2 solutions:

0.322, 2.36 (2d.p.)

I can get the first solution, but not the second. Help!!

Apr 10, 2015

#7
+95177
+5

Thanks guys :)

I really like that you have interacted with the answerers anon, I wish a lot more people did that.

Sometimes we feel like we are teaching thin air.   :))

Apr 11, 2015

#1
+17747
+5

cos(2x + 0.464)  =  1

2x + 0.464  =  cos-1(1)

But:  cos-1(1)  =  0   ---   and only 0, so there will  be only one answer within that domain.

And:  2x + 0.464  =  0     --->     2x  =  -0.464     --->     x  =  -0.232

To get within the domain, add 3.14159   --->   x  =  2.909.

Apr 10, 2015
#2
+5

You missed the square root in front of the equation, so with it, what I got was:

2x + 0.464 = cos^-1 (1 / sqrt5)

2x + 0.464 = 1.107

2x = 0.643

x = 0.322

Even if you add pi to this answer, you don't get the next solution. So where does 2.36 come from? :(

Apr 10, 2015
#3
+17747
+5

I did miss the √5 --- thanks for the correction!

When you (corectly!) got step 2 to equal 1.107  -- because it's cosine, you get two answers both + and - 1.107

Apr 10, 2015
#4
+5

Hmm still no luck. I'm not sure why you'd also get a negative 1.107?

It doesn't give the correct answer though.

2x + 0.464 = -1.107

2x = -1.571

x = -.7855

We are supposed to be getting 2.36 :(

Apr 10, 2015
#5
+27336
+5

cosine is positive in the first and fourth quadrants, so the angle whose cosine is 1/√5 is not just 1.107, but also -1.107.  However, this angle can also be expressed as 2pi - 1.107.  Using 2pi - 1.107 should give you the other solution in the range 0 to pi.  (Most calculators/software will just give one value when asked for cos-1 .)

See image:

.

Apr 10, 2015
#6
+94526
+5

√5cos(2x + 0.464)  =  1      let 2x + 0.464 = θ   divide both sides by √5

cos θ  = 1/√5    using the cosine inverse, we have

cos-1(1/√5) = 1.107  and 5.176 = θ

So

2x + 0.464  = 1.107     subtract 0.464 from  both sides

2x = .643      divide both sides by 2

x = .3215  or about .322 rounded

And

2x + 0.464  = 5.176

2x = 4.712

x = 2.356 or about 2.36 rounded

Apr 10, 2015
#7
+95177
+5

Thanks guys :)

I really like that you have interacted with the answerers anon, I wish a lot more people did that.

Sometimes we feel like we are teaching thin air.   :))

Melody Apr 11, 2015