Alg 2 BC U13Days 1-4 Fundamental Trig Identities

An identity is an equation that is true for every value in the domain of the variable.

Reciprocal Identities:

Quotient Identities:

Pythagorean Identities:

Negative Angle Identities:

These identities are useful for (among other things):

  1. Finding values of trig functions (from values of OTHER trig functions)

Ex: If is in Quadrant IV, find the value of the

  1. Simplifying trig expressions

Ex: Express as a single trig function: =

  1. VERIFYING trig expressions

Ex: Verify the identity:

Problem Set #1:

1. If and is in quadrant II, find the values of:

a) secb) sin c) cot(-)

2. Given csc = , and is in quadrant III, find

a) cotb) cosc) tan(-)

3. Write the following in terms of sine and cosine, then simplify:

a) b)

c) d)

Using Algebra with Trigonometry:

Common Denominators: This is needed for adding or subtracting fractions

FOIL:

Conjugates: This is helpful because it can create a Pythagorean identity.

Factoring: You can use difference of squares, British Method, GCF

Remember: You can always split a numerator. You can NEVER split a denominator!

Problem Set #2: Simplify each expression to a single trig function, power of a trig function or constant:

1.3.

2.4.

5.6.

7.8.

9. 10.

VERIFYING IDENTITIES – You are really doing a ______and therefore need ______.

Some helpful hints:

  1. You must work with ______of the equation.
  1. It is usually easiest to work with the ______side of the equation.
  1. Do the ______!! (factor, add fractions, square a binomial, etc)
  1. Watch for ______IN THEIR VARIOUS FORMS.
  1. If all else fails, convert all terms to ______.

6.Don’t just stare at the problem. Try something! Even paths that lead to dead ends giveinsight.

Example #1:

Example #2:

Problem Set #3: Verify each identity, giving a reason for each step.

  1. 2.

3.4. sec 2 tan 2 + sec 2 = sec 4

5.6.

7.

Match the expressions below to one in the box at right: (You do not need to give reasons for these.)

1.

2.

3. 4.

5.

Problem Set #4: Verify each identity, giving a reason for each step:

1. 2.

3. 4.

5. 6.