Find all solutions of the equation in the interval [0, 2pi). sinx = 1 - cosx

Write your answer(s) in radians in terms of t.
If there is more than one solution, separate them with commas.

Step-by-step explanation:

Begin by squaring both sides to get rid of the radical. Doing that gives you:

Now use the Pythagorean identity that says

and make the replacement:

. Now move everything over to one side of the equals sign and set it equal to 0 so you can factor:

and then simplify to

Factor out the common cos(x) to get

and there you have your 2 trig equations:

cos(x) = 0 and 1 - cos(x) = 0

The first one is easy enough to solve. Look on the unit circle and see where, one time around, where the cos of an angle is equal to 0. That occurs at

The second equation simplifies to

cos(x) = 1

Again, look to the unit circle and find where the cos of an angle is equal to 1. That occurs at π only.

So, in the end, your 3 solutions are

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question: which best states the author’s purpose for including this information in the text?

answer: to challenge the reader’s ideas about a historical event