Module 5 Project: Trig Values and Graph Characteristics Answers Part A 1. Sine !
a. 0 k. −
!
!
!
!
!
!
b. ! c. ! d. ! e. 1 f. ! g. ! h. ! i. 0 j. − ! !
!
l. −
!
!
m. -­‐1 n. −
!
!
o. −
!
!
!
p. − ! q. 0 Cosine !
a. 1 k. −
!
!
!
b. ! c. ! d. ! e. 0 f. − ! !
!
!
l. − ! m. 0 !
n. ! !
g. −
!
h. −
!
!
!
i. -­‐1 j. −
!
!
!
o. ! p. ! q. 1 Tangent !
a. 0 b. ! c. 1 d. 3 e. und f. − 3 g. -­‐1 h. −
k. 1 l. 3 m. und n. − 3 o. -­‐1 p. −
2. Graph 1 = tangent Graph 2 = sine !
!
!
!
!
i. 0 j. ! q. 0 Graph 3 = cosine 3. Cosine is a shift of 𝜋 2 to the left from sine. OR Sine is a shift of 𝜋 2 to the right from cosine. Part B 1. amplitude = 3 !
2. amplitude = ! !
period = π horizontal shift = ! to the right vertical shift = 2 down !!
horizontal shift = 2 to the right vertical shift = 1 up
period = π horizontal shift =none vertical shift = 2 down period = 2π horizontal shift = ! to the left period = 2π horizontal shift = ! to the right period = ! (reflection on the x axis) !
3. amplitude = ! 4. For a sine graph amplitude = 2 !
vertical shift = 1 up !
vertical shift = 1 up For a cosine graph amplitude = 2