# The Calculus Page Problems List

[mage lang=”” source=”flickr”]the calculus page problems list[/mage]
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So, I have to take my pre-calculus midterm exam tomorrow, so I am in the middle of doing the exam review papers now…I got to the 1 page and don’t remember even learning this.
Can anyone help, but don’t just put the answers (I have the answers) can you tell me how to do these problems. I’ll list the questions with the answers.
(^2 = squared)

Without using a calculator, find all the solutions in the interval [0, 2 pi)

Q1: 2sinx cosx – cosx = 0
Answer: 90, 270, 30, 150

Q2: sin^2 x = 1

Q3: 2sin^2 x – 5sinx – 3 = 0

Thank you for your help and explanation

1)

2sinx cosx – cosx = 0

cosx[2sinx – 1] = 0

so cosx = 0 or 2sinx – 1 = 0

when cosx = 0

x = 90 or 270 degrees

when 2sinx – 1 = 0

sinx = 1/2

so x = 30 or 150 degrees (sin is positive in 1st and 2nd quadrants)

All the values of x are 30, 90, 150 and 270 degrees

2)

sin^2(x) = 1

take square root

sinx = 1 or -1

x = 90 or 270 degrees (positive in 1 and negative in 3rd qyadrants)

3)

2sin^2(x) – 5sinx – 3 = 0

2sin^2(x) – 6sinx + sinx – 3 = 0

2sinx(sinx – 3) + 1(sinx – 3) = 0

(sinx – 3)(2sinx + 1) = 0

sinx = 3 ( which is invalid since sinx lies between – 1 and + 1)

2sinx + 1 = 0

sinx = -1/2

x = (180 + 30) or (360 – 30) ( sin is negative in 3rd and 4th

x = 210 or 330 degrees

Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007
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