# Trig Question: Exact value of

Trig Question: Exact value of ......

## Homework Statement

Find the exact value of:

sin(11"pi" / 2)

without a calculator.....

## The Attempt at a Solution

I don't understand how to solve this with the unit circle. What is my first step here?? My text book just gives the answer, and not how to solve it.

THanks for any help!

## Answers and Replies

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try converting 11pi/2 into degrees then looking at the unit circle

eumyang
Homework Helper

Find the angle in [0, 2π) that is coterminal to 11π/2.

As an example, if I wanted to find cos(15π/4), I note that
cos(15π/4) = cos(7π/4)
and this angle is in [0, 2π), so it's straight forward to evaluate it.
cos(7π/4) = √2/2

You'll have to do something similar in your problem.

## Homework Statement

Find the exact value of:

sin(11"pi" / 2)

without a calculator.....
If you start at zero and rotate the radius through that angle, where does it end up? (The "exact value without a calculator" is a hint that it will be equal to one of the common angles.)

Here is what I came up with....Im sure there is a better way of solving this!

TO convert into degrees, I get 990. So, thats 360 + 360 + 270, which according to the unit circle is (0,-1), so since its sin, the answer will be -1

That seems like the wrong way of firguring this out.....

But how does 11pi/2 equate to 3pi/2

eumyang
Homework Helper

But how does 11pi/2 equate to 3pi/2
Read up on coterminal angles in your textbook (assuming you have one).

11*pi/2

A quarter revolution in radians of the unit circle is half a pi (since four quarters aka a complete revolution is 2pi)

Now just start counting :)

"But how does 11pi/2 equate to 3pi/2"
One revolution of the unit circle is 2 pi, therefore wherever you are, you can go 2pi around, you end up in the exact same spot. Any n*pi/2 -/+ 2pi = n*pi/2 is exactly the same if used in a trigonometric function

Last edited:
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor

Here is what I came up with....Im sure there is a better way of solving this!

TO convert into degrees, I get 990. So, thats 360 + 360 + 270, which according to the unit circle is (0,-1), so since its sin, the answer will be -1

That seems like the wrong way of firguring this out.....

But how does 11pi/2 equate to 3pi/2
You can do the same thing without bothering to convert to degrees first. Every time you go around the circle corresponds to $2\pi$, so subtract off multiples of $2\pi$. What does that leave you?

If you start at zero and rotate the radius through that angle, where does it end up? (The "exact value without a calculator" is a hint that it will be equal to one of the common angles.)
Or it could refer to sum, difference, half or double angle identities.

mege

Personally, I find the unit circle very helpful, but you could graph the function in an x-y plot (I'm presuming you understand the period of the sin function at least visually).