Finding the intercept between a straight line and a cosine curve.

[Another random user]

Hello, as you may have guessed, I am new here so ill apologise in advance if I posted in the wrong thread.

I had gotten stumped on a bit of an assignment where I need to find the intercept between a straight line and a cosine curve, except that the equation for the cosine curve is rather full on and I tried rearranging the Eqn as per normal as shown in the attachment

If I went wrong somewhere could you please correct me.

Thanks in advance

 

[tkhunny]

First: Significant Figures. You CANNOT switch from 0.145 = 0.855 cos(stuff) to 29/171 = cos(stuff). The correct result might be 0.170 = cos(stuff).

Second: You have not recognized that the cosine takes on the desired value:

a) Twice for EACH period, and
b) For infinitely many periods.

The Inverse Cosine function (on your calculator) will give one result in the 1st or 2nd Quadrant. It is your responsibility to find the other solution in Quadrant III or IV.

 

[mmm4444bot]

I see two mistakes, in your work. I have outlined them in red (in order).

The first mistake is bad notation only (i.e., it did not introduce any error because you didn't actually do what you wrote).

The second is an algebraic mistake that needs to be corrected.

1) Do not place the subtraction operator inside grouping symbols; otherwise, you're showing that -22*Pi/69 is being multiplied by 100*Pi*x/621 instead of subtracting 22*Pi/69 from 100*Pi*x/621.

2) You need to multiply the entire left-hand side of the equation by 621. You multiplied only 22*Pi/69 by 621.

Fix the second mistake, and you'll get the correct value for x (a value between 4.5 and 5). :cool: