Solve -10 cos(3t )= 7 on [-2,5], Mathematics

Assignment Help:

Solve -10 cos(3t )= 7 on [-2,5].

Solution

Let's first get the inverse cosine portion of this problem taken care of.

cos(3 t )= -  7/10            ⇒     3t = cos-1( - 7 )= 2.3462

Don't forget that still we need the "3"!

Now, let's look at a rapid unit circle for this problem.  Since we can illustrates the angle 2.3462 radians is in the second quadrant and the other angle that we need is in the third quadrant. We can find this second angle in accurately the same way we did in the previous instance. We can use either -2.346vor we can utilizes 2π - 2.3462 =3.9370.  As with the previous instance we'll utilizes the positive choice, however that is purely a matter of preference.  You could utilize the negative if you wanted to.

1172_circle28.png

Thus, let's now finish out the problem.  Firstly, let's acknowledge that the values of 3t that we need are,

3t = 2.3462 + 2π n

3t = 3.9370+ 2π n

n = 0, ±1,±2,.........

Now, we have to properly deal along with the 3, hence divide that out to get all the solutions to the trig equation.

t = 0.7821 +(2π n/3)

t = 1.3123 +(2πn/3)

n = 0, ±1, ±2,..........

At last , we have to get the values in the given interval.

n = -2 :  236_trig unit.png          and           -2.8765

 n = -1 :t = -1.3123    and               -0.7821

n = 0    :t = 0.7821       and      1.3123

 

n = 1    :t = 2.8765       and      3.4067

n = 2    :                                t =4.9709            and      5.5011

The solutions to this equation, in the specified interval are then,

t = -1.3123, - 0.7821, 0.7821, 1.3123, 2.8765, 3.4067, 4.9709

We've done a couple of basic problems with cosines, now let's take a look at how solving equations with sines work.


Related Discussions:- Solve -10 cos(3t )= 7 on [-2,5]

Proof integral function, Proof of: if f(x) > g(x) for a x b th...

Proof of: if f(x) > g(x) for a x b then a ∫ b  f(x) dx > g(x). Because we get f(x) ≥ g(x) then we knows that f(x) - g(x) ≥ 0 on a ≤ x ≤ b and therefore by Prop

Geometry, Can two lines contain a given point

Can two lines contain a given point

Decimals, 0.875 of a number is 2282. What is the number ?

0.875 of a number is 2282. What is the number ?

Geometry, how can you tell qhich trangle is sss,asa, sas, and aas s

how can you tell qhich trangle is sss,asa, sas, and aas s

Show that cos12+cos60+cos84=cos24+cos48 , L.H.S. =cos 12+cos 60+cos 84 =c...

L.H.S. =cos 12+cos 60+cos 84 =cos 12+(cos 84+cos 60) =cos 12+2.cos 72 . cos 12 =(1+2sin 18)cos 12 =(1+2.(√5 -1)/4)cos 12 =(1+.(√5 -1)/2)cos 12 =(√5 +1)/2.cos 12   R.H.S =c

The alternative hypothesis, The alternative hypothesis When formulatin...

The alternative hypothesis When formulating a null hypothesis we also consider the fact that the belief may be found to be untrue thus we will refuse it.  Therefore we formula

Organized list strategy, i can not figer out my homework it says "USE THE M...

i can not figer out my homework it says "USE THE MAKE AN ORGANIZED LIST STRATEGY,Medeline bikes 4 laps around her neighborhood 2 times a week.How many laps does she bike in 8 weeks

Determine the probability that is of low quality, 1) A local factory makes ...

1) A local factory makes sheets of plywood. Records are kept on the number of mild defects that occur on each sheet. Letting the random variable x represent the number of mild de

Quadratic equations by completing the square method, Can we solve the Quadr...

Can we solve the Quadratic Equations by completing the square method? if yes explain it.

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd