Question

can someone verify that Example 1 on this site has an error?
http://tutorial.math.lamar.edu/Classes/CalcI/TrigEquations_CalcII.aspx

I think the second angle is suppose to be 1.5344 and not 2.5345

Answer 1

How do you figure?

2x - 1 = 2.2143 + 2πn
2x - 1 = 4.0689 + 2πn

2x = 2.2143 + 2πn + 1 = 3.2143 + 2πn
2x = 4.0689 + 2πn + 1 = 5.0689 + 2πn

x = (3.2143 + 2πn) / 2 = 1.60715 + πn (mult. both 3.2143 and 2πn by 1/2)
x = (5.0689 + 2πn) / 2 = 2.53445 + πn (mult. both 5.0689 and 2πn by 1/2)

Answer 2

well i got 2x-1 = 2.2143 so i added one first to both side, getting 2x = 3.2143 + 2πn for my first angle. and the second angle would be 2π - 3.2143 = 3.0689
so x = 1.5344 + πn

Answer 3

Well, if you take the x that you calculated (i.e. 1.5344 + πn) where n = 0, you'll notice that when you put it back into cos(2x - 1) it doesn't equal -3/5. So, your answer is incorrect. And it is probably because you either didn't have your calculator in radians or you took the x you calculated, which by the way is NOT the angle (2x - 1 is) and subtracted 2π from it which will give you an incorrect answer.

I checked both the answers for x in the example and they both equate to ≈ -3/5 = -0.6

Answer 4

you're right, I found my mistake. I changed the angle when I added 1 before calculating for the second angle.
Thankss!