- anonymous

How do you express trigonometric functions of degrees in terms of a reference angle? Please use the following as examples:
4a. cot 285º b. sec -105º c. csc 600º d. tan 3º
6a tan 160º b. csc 115º c. sec 235º d. cot 5º

- katieb

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- Mertsj

The reference angle is the angle the terminal side of the angle makes with the x axis.

- Mertsj

So let's begin. It helps to draw them

- Mertsj

|dw:1328759040338:dw|

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## More answers

- anonymous

you mean 285º?

- Mertsj

|dw:1328759118643:dw|

- Mertsj

No. I meant 270. that's why there was 15 to go.

- anonymous

i see. thanks!
what is the terminal side of the angle?

- Mertsj

|dw:1328759258167:dw|

- Mertsj

Ready for the next one?

- anonymous

OH. thank you so much! yes.

- Mertsj

|dw:1328759377288:dw|

- Mertsj

Same reference angle as the first one.

- anonymous

ok.

- Mertsj

Now that we can draw them, we need to pay attention to the directions and the signs.

- Mertsj

285 degrees. That angle is in quadrant 4. The reference angle is 75 degrees. So the cotangent of 285 is the same as the cotangent of 75 except for the sign.

- Mertsj

All functions are positive in the first quadrant and all reference angles will be first quadrant angles. However, the cotangent is negative in the fourth quadrant so we have to write:
\[\cot (285)=-\cot(75)\]

- Mertsj

Are you with me?

- anonymous

yes.

- anonymous

i guess i'm a little confused with the quadrant thing...

- Mertsj

Do you know that the cos is like x and the sin is like y?

- anonymous

I didn't...

- anonymous

what else should I know?

- Mertsj

that tan = y/x
cot=x/y
sec=1/x
csc=1/y

- Mertsj

Knowing that will help you find the sign of the functions in the various quadrants.

- anonymous

ok, thank you... i don't think I had the hang of that either.

- Mertsj

For example: since the sec is the reciprocal of the cos, it will be positive in quadrants 1 and 4 because that is where x is positive.

- anonymous

I see.

- Mertsj

So let's do the next one
sec(-105)=

- Mertsj

We have seen that -105 is a third quadrant angle. Will the secant be positive or negative in the third quadrant? Remember the sec agrees with the cos that the cos is like x

- anonymous

the secant will be negative right?

- Mertsj

yes. So we would write:
\[\sec(-105)=-\sec(75)\]

- anonymous

could you write it as sec(-75) or would that be wrong?

- anonymous

also, i just rechecked the book and 4d is actually in radians (tan=3) and 6d is also in radians (cot=5) how do we do those? I understand the degrees now... but i don't understand the radians.

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