Problem with value of tangent on the trig circle

[bbm25]

 

[Dr.Peterson]

Have you learned to rationalize the denominator? That's all it's doing differently!

 

[bbm25]

i made mistakes. For the diagram, the square roots should be for numerators only and not the whole fractions.

 

[bbm25]

Have you learned to rationalize the denominator? That's all it's doing differently!

 

[HallsofIvy]

Whether it is "necessary" or not depends upon whether or not your teacher marks you down for not doing it! Outside of that, while it is not necessary to rationalize the denominators (\(\displaystyle \frac{1}{\sqrt{3}}= \frac{\sqrt{3}}{3}\) means that they are just different ways of saying the same thing.) since such things as adding fractions involves combining denominators, It is more convenient.

 

[MarkFL]

I don't worry much about rationalizing a denominator unless I'm helping a student who has been instructed to do so. In the days of tables of square roots, a rationalized denominator made using such tables much easier, but now with digital computing devices, it's not an issue.

 

[Dr.Peterson]

I always say that how (and whether) you simplify a result depends on what you plan to do next.

For some purposes, it's better to leave the radical in the bottom (as in a case I helped a student with just today, where the next step was to take the reciprocal!). But if the next step is to check your answer against the back of the book, rationalizing denominators can be a good idea ... because the main benefit is to be able to compare more easily by putting everything in a standard form.