How Do You Convert Sin and Cos Values to Tan in Trigonometry?

[CrossFit415]

Homework Statement

(sin 20° / cos 380°) + tan 200°

Homework Equations

tan = sin / cos

The Attempt at a Solution

Ok so.. I know tan = sin / cos. How do I convert sin 20° / cos 380° into tan? What should I do with the numbers? Thanks

 

[tiny-tim]

Hi CrossFit415!

Trig tables only go up to 90°

… so they want you to convert all the angles to ≤ 90° ! ​

 

[HallsofIvy]

What, someone actually uses tables to find trig values?

CrossFit415, what, exactly are you asked to do? If just find the value of that, why change anything, why not just put the numbers into a calculator? (Being sure it is in degree mode, of course.

(Yes, I see that 380= 360+ 20 but I don't see that that helps.)

 

[CrossFit415]

Yea but I can't use a calculator. I just wanted to know how to manually convert them. Thanks

 

[eumyang]

I'm assuming that we could leave the answer as a multiple or power of a trig function.

OP: you were told in one of your other threads what to do with coterminal angles. From what HallsofIvy post, you can see that
\frac{\sin 20^{\circ}}{\cos 380^{\circ}} + \tan 200^{\circ}
= \frac{\sin 20^{\circ}}{\cos 20^{\circ}} + \tan 200^{\circ}

Also, what can you do with tan 200°? (Hint: it's not the same as what can be done with sine and cosine, because the period of tangent is different.)

 

[ebits21]

What is the reference angle for 380 degrees? Think how that relates to the sin of 20 degrees and tan.

The value for tan should pop out at you!

Edit: Then think about what the reference angle for 200 degrees is.