Question

Answer the following.(a) Find an angle between 0° and 360° that is coterminal with 1260°(b) Find an angle between 0 and 2pi that is coterminal with-23pi/12Give exact values for your answers.

Answer 1

`\begin{gathered} a)\text{ 180 deg} \\ b)\text{ }(\pi)/(12) \end{gathered}`

Step-by-step explanation:

a) Here, we want to find an angle between 0 and 360 degrees that is coterminal with 1260

To find angles coterminal with an angle, what we have to do is to subtract multiples of 360 degrees from it

Now, let us find the number of times we can have 360 in 1260

By division, we have it that 1260/360 = 3.5

Now, to find the coterminal angle within the range, we have it that:

`1260-3(360)\text{ = 1260-1080 = 180}`

The coterminal angle within the given range is 180 degrees

b) Mathematically, we know that the term "pi" represents 180 degrees

Thus 2 pi is same as 2 * 180 = degrees

For ease of convenience, let us have the angle given in degrees

We have this as:

`(23*180)/(12)\text{ = -345 }`

Now, let us proceed

What we have to do is to add this to 360 degrees so we can get the positive coterminal in degrees

We have this as -345 + 360 = 15

Lastly, we represent this in radians as follows:

`(\pi)/(12)`