If , what is equal to?

Attempt:

Since , so:

but think I made a mistake without considering the interval it in. What should I do

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- Nov 9th 2010, 02:49 PM #1

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- Nov 9th 2010, 03:30 PM #2

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is the third quadrant,

If you draw a unit-radius circle, then in that 3rd quadrant, pick a point on the circumference.

draw a right-angled triangle by drawing lines from the point directly up to the x-axis

and directly from the point to the circle centre.

For this triangle, angle at the centre inside the triangle.

adjacent

opposite

hypotenuse

Draw a second right-angled triangle, whose base is and whose opposite is in that same 3rd quadrant

which is the angle after one revolution in the 3rd quadrant.

There is another angle in the 2nd quadrant, as cosine is negative there also.

From there, the range of angles can be deduced from

- Nov 9th 2010, 04:28 PM #3

- Nov 9th 2010, 11:19 PM #4

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- Nov 10th 2010, 02:08 PM #5

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Better to start from scratch,

we can ascertain the graph of

Notice that

This means the slope of the graph is , depending on whether is positive or negative.

Hence, it is a periodic triangle wave.

For

goes from

Therefore goes from which is from

If you have an exact value for , then since the graph is rising linearly from , then