Trig Problems

[mat3]

I am stuck on a couple of problems.
For example What is the exact value of the trig function tan(-510) :?:

 

[tkhunny]

Think "reference angle".

The general idea is to unwrap it until you get somewhere you recognize. 360° = 1 Unwrap.

-510°
-510° + 360° = -150° Recognize it yet?
-150° + 360° = 210° Recognize it yet?

That's Quadrant III, reference angle 30°.

sin(210°) = -1/2
cos(210°) = -sqrt(2)/3
tan(210°) = sin(210°)/cos(210°)

 

[mat3]

So is tan(30) an exact value? Or should I use tan (210)?

Thanks

 

[mat3]

Also should I leave it as tan(210) or as .5774. :?

 

[tkhunny]

tan(30°) is not the right answer. 30° is the Reference Angle. It is your responsibility to put it in Quadrant III. Sine and Cosine are negative in Quadrant III. Tangent is positive.

I left you one tiny step short of the answer. Substitute the given values and get the EXACT answer.

Note: 0.5774 is NOT an exact answer.
Note: tan(210°) IS an exact answer, but not very interesting.

 

[mat3]

Thank you so much