# How To Solve Trigonometry Problems

Step 3: Show the sizes of the other angles and the lengths of any lines that are known.Step 6: Decide whether you will need the Pythagorean theorem, sine, cosine or tangent. The hypotenuse is the longest side in a right triangle.

As you gain more practice, you can skip or combine these steps when you recognize other identities.

STEP 1: Convert all sec, csc, cot, and tan to sin and cos.

Most of this can be done using the quotient and reciprocal identities.

STEP 2: Check all the angles for sums and differences and use the appropriate identities to remove them.

The trick to solve trig identities is intuition, which can only be gained through experience.

The more basic formulas you have memorized, the faster you will be.

The angle of elevation of a hot air balloon, climbing vertically, changes from 25 degrees at am to 60 degrees at am.

The point of observation of the angle of elevation is situated 300 meters away from the take off point.

Some teachers will ask you to prove the identity directly (from one side to the other in a straight line).

In what follows, it is assumed that you have a good grasp of the trig-ratio values in the first quadrant, how the unit circle works, the relationship between radians and degrees, and what the various trig functions' curves look like, at least on the first period.