If cos(x)=3/5 and x is in quadrant 1, then find exact values for (without solving for x):

Question

A. Sin(2x)

B. Cos(2x)

C. Tan(2x)

Answer 1

Draw a figure.

In a right triangle where the cos of one of the angles is 3/5.

The other side is 4.

You should know this immediately because of the so-called 3-4-5 triangle is so frequently encountered and if you do not know this, the you should easily compute it from the theorem of Pythagoras.

Given this information you can now easily computer all the other 5 trig functions.

The you need the double angle formulae to answer your question.

sin 2x = 2 sin x cos x and cos 2x = cos² x - sin²x.

If you are not ever going to study more mathematics, you need to learn/memorize this information for subsequent tests; if you are going on in mathematics at all, you will need to learn/memorize this information which you will use very frequently.