Standardized Test Practice
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Consider each side of the equation as a function. Graph both functions on the same coordinate plane and look for points of intersection.
t≈ 2.52
To solve the given equation in the interval from 0 to 2π, we will consider both sides of the equation as functions. Then, we will graph both of them on the same coordinate plane. 3cos t/3= 2 ⇓ y= 3cos t/3 and y= 2 Before graphing the functions, note that the amplitude of the cosine function is 3. Also, we want to find solutions between 0 and 2π ≈ 6.28. Accordingly, let's resize the window of the calculator to show y-values between - 3.5 and 3.5, and x-values between 0 and 6.28. To do so, we will push WINDOW and change the settings.
We can see that there is one point of intersection. To find this, push 2nd and CALC and choose the fifth option, intersect.
While using the intersect tool, we are asked to select the first function, the second function, and to make a guess for the approximate point of intersection. Because there is only one point of intersection between these two functions, we can just start with any point in our domain, that is from 0 to 2Ï€.
The point of intersection is approximately 2.523206, which we will round to be t≈ 2.52. We also see, that there are no more intersections in the given domain. t≈ 2.52
Since we obtained a true statement, we know that the solution is correct.