Chapter 10 - NCPN

Ongoing Assessment
Find the exact value of cos 240°. − 1 2
Example 2
Using Angle Sum and
Difference Identities
Find the value of the expression sin 110° cos 65° – cos 110° sin 65°.
Solution
Use the angle difference identity sin(A – B) = sin A cos B – cos A sin B to
evaluate the expression.
sin(A – B) = sin A cos B – cos A sin B
sin(110° – 65°) = sin 110° cos 65° – cos 110° sin 65°
sin(110° – 65°) = sin 45° =
2
2
So sin 110° cos 65° – cos 110° sin 65° =
Ongoing Assessment
2
2 .
Find the value of the expression sin 160° cos 110° + cos 160° sin 110°. –1
Lesson Assessment
Think and Discuss
see margin
1. Is sin (A + B) = sin A + sin B If not, give a counterexample.
2. Is cos (A + B) = cos A + cos B If not, give a counterexample.
3. What expression is equal to sin (A – B)
4. Explain how to use a difference identity to find the exact value of
sin 142° cos 112° – cos 142° sin 112°.
5. Explain how to use mental math and a sum identity to find the
exact value of cos 71° cos 19° – sin 71° sin 19°.
476 Chapter 10 Trigonometric Functions and Identities