Download PCM 12 Chapter 6 Trigonometric Identities. Name: For the sum of

PCM 12
Chapter 6 Trigonometric Identities.
Name:__________________
Lesson Notes: 6.2: Sum, Difference, and Double-Angle Identities
For the sum of any two angles A and B, we have the addition formulas:
Replacing B by −B in the addition formulas and using the relations sin (−θ) = −sin θ and
cos (−θ) = cos θ from Section 1.5 gives us the subtraction formulas:
This, combined with replacing B by −B and using the relation tan (−θ) = −tan θ, gives us the
addition and subtraction formulas for tangent:
Example 1) Write each expression as a single trigonometric function.
Example 2) Determine an identity for cos 2A that contains only the cosine ratio.
Example 3) Determine an identity for cos 2A that contains only the sine ratio.
Example 4) Prove that
Example 5) Determine the exact value for each expression.
Pre-Calculus 12
Unit 6.2 Assignment.
Name:_____KEY_______
1. Write each expression as a single trigonometric function.
2. Simplify and then give an exact value for each expression.
3. Write each expression as a single trigonometric function.
4. Simplify each expression to a single primary trigonometric function.
5. Angle θ is in quadrant II and sin θ =
following.
. Determine an exact value for each of the
6. If (sin x + cos x)2 = k, then what is the value of sin 2x in terms of k?
7. Show that each expression can be simplified to cos 2x.