NAME:_______________________________________________
Algebra 2/Trig – Finding the Exact Value with Sum/Difference Identities CLASSWORK
DATE:__________
PERIOD:________
DO NOW: Answer the following questions in order to prepare for today’s lesson.

1.
2. If
Where are the Sum and Difference Identities found?
Evaluate in radical form:
and x is in quadrant II,
, and y is an acute angle, find the value of
.
LEARNING GOAL: To Find the Exact Value of Trig Functions by Using
the Sum/Difference Identities
TRIGONOMETRY RADICALS IN THE FIRST QUADRANT
DIRECTIONS: Express the following solutions as exact values (no decimals).
30°
45°
60°
sin 
cos 
tan 
Example: Express, as a single fraction in simplest form, the exact value of cos 75°.

How can we rewrite 𝟕𝟓° using the 𝟑𝟎°, 𝟒𝟓°, 𝟔𝟎° from the first quadrant?
cos(75) = cos(30 + 45)
cos(𝐴 + 𝐵) = cos 𝐴 cos 𝐵 − sin 𝐴 sin 𝐵
cos(30 + 45) = cos 30 cos 45 − sin 30 sin 45
1. Express, as a single fraction in simplest form, the exact value of sin 15°.
 How can we rewrite this function using the special 𝟑𝟎°, 𝟒𝟓°, 𝟔𝟎° from the first quadrant?
2. Express, as a single fraction in simplest form, the exact value of tan 105°.