How do I solve sin(30)*tan(60)-cos(30) without a calculator?

[LambdaVoid]

Could someone tell me how to solve it step by step? I tried looking elsewhere for formulae, but didn't find anything.
Also try to explain it as simply as possible.

 

[Dr.Peterson]

Check your textbook, notes, or search elsewhere for "trig special angles".

Then show us what you find, and make an attempt to use it to solve the problem. Then we can start to help.

 

[topsquark]

You should either keep a list or memorize the sine, cosine, and tangent of the angles 0, 30, 45, 60, 90 degrees. They come up a lot.

-Dan

 

[JeffM]

You should either keep a list or memorize the sine, cosine, and tangent of the angles 0, 30, 45, 60, 90 degrees. They come up a lot.

-Dan

Actually, all you need to do is memorize the values for the sine at angles 0, 30, 45. 60, and 90 degrees because

[math]\sin (\theta \text { degrees}) = \cos (90 \text { degrees} - \theta \text { degrees})\\ 0 \le \theta < 90 \implies \tan ( \theta \text { degrees}) = \dfrac{\sin ( \theta \text { degrees})}{\cos ( \theta \text { degrees})}[/math]

 

[The Highlander]

Could someone tell me how to solve it step by step? I tried looking elsewhere for formulae, but didn't find anything.
Also try to explain it as simply as possible.

Hi LambdaVoid,

Have a look at the attached picture and make a copy of the triangle diagrams into your workbook (or whatever). You don't need to copy the text in the picture, unless you want to (as a useful reminder of what was going on at a later date), and then copy out and fill in the Ratios derived from these diagrams for the Sines, Cosines & Tangents of 30°, 45° and 60°.

These are the Exact Values everyone is telling you that you ought to know.

This is a useful way to remember how to get them (from first principles) using a couple of simple triangles; one Isosceles & one Equilateral (split in two).

I'll give you a start on how to fill in the blanks:-

Sin 45° = \(\displaystyle \frac{1}{\sqrt2}\) & Sin 60° = \(\displaystyle \frac{\sqrt3}{2}\) . Continue..........

(You should also know the appropriate values for all the Trig Ratios at 0° & 90° from when you first learned about the topic; if not just stick those into a calculator but pay special attention to the "answer" that comes up for Tan 90°; it is not zero!)

Once you insert the relevant exact values that you have now "discovered" (still in fractional form) into your original expression [sin(30)*tan(60)-cos(30)], the rest is just Arithmetic (that should not require a calculator).

Show us how you get on, please.