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Honors Pre-‐calculus Name __________________________________
Test Review -‐ Unit 6 Part 2 Date ______________________ Pd. _________
Find the exact values of each expression. Show all work!
1) 𝒄𝒐𝒔 𝟓𝝅𝟖 ____________
2) 𝒄𝒐𝒔 𝟕𝟎°𝒄𝒐𝒔 𝟒𝟎° + 𝒔𝒊𝒏 𝟕𝟎°𝒔𝒊𝒏 𝟒𝟎° ____________
3) 𝒔𝒊𝒏 − 𝝅𝟏𝟐
____________
4) 𝒕𝒂𝒏 𝟐𝟎°!𝒕𝒂𝒏 𝟐𝟓°𝟏!𝒕𝒂𝒏 𝟐𝟎°𝒕𝒂𝒏 𝟐𝟓°
____________
5) sin 105° _____________
6) cos 22.5° __________
Use the information about given angles α and β to find the exact values of parts a-‐h. Show all work!
7) 𝒔𝒊𝒏 𝜶 = − 𝟐𝟑, 𝝅 < 𝛼 < !!
!; 𝒄𝒐𝒔 𝜷 = − 𝟐
𝟑 , 𝝅 < 𝛽 < !!
!
a) 𝒔𝒊𝒏 𝜶 + 𝜷 _______________
b) 𝒄𝒐𝒔 𝜶 + 𝜷 _______________
c) 𝒔𝒊𝒏 𝜶 − 𝜷 _______________
d) 𝒕𝒂𝒏 𝜶 + 𝜷 _______________
e) 𝒔𝒊𝒏 𝟐𝜶 _______________
f) 𝒄𝒐𝒔 𝟐𝜷 _______________
g) 𝒔𝒊𝒏 𝜷 𝟐 _______________
h) 𝒄𝒐𝒔 𝜶𝟐 _______________
Express the product as a sum containing only sines or cosines.
8) cos(4θ) cos (2θ) ____________________________________________________
Express the sum or difference as a product of sines and/or cosines.
9) sin(4θ) – sin(2θ) ____________________________________________________
Solve each equation on the interval 0 ≤ θ ≤ 2π.
10) 𝟐 𝐜𝐨𝐬𝜽 + 𝟐 = 𝟎 ____________________________________________________
11) 𝒄𝒐𝒔 𝜽 = 𝒔𝒆𝒄 𝜽 ____________________________________________________
12) 𝟐𝒄𝒐𝒔𝟐 𝜽 + 𝒄𝒐𝒔 𝜽 − 𝟏 = 𝟎 ____________________________________________________
13) 𝐬𝐢𝐧 𝟐𝜽 = 𝟐 𝐜𝐨𝐬𝜽 ____________________________________________________
Find the exact value. Show all work!
14) 𝒄𝒐𝒔 𝒕𝒂𝒏!𝟏 −𝟏 + 𝒄𝒐𝒔!𝟏 − 𝟒𝟓
_______________
15) 𝐬𝐢𝐧 𝟐 𝐜𝐨𝐬!𝟏 − 𝟑𝟓
_______________
Solve the Identities
1) 𝑠𝑒𝑐! !!= !
!!!"#!
2) tan 2𝜃 tan 6𝜃 = !"#!!!!"#!!!"#!!!!"#!