Use one of the identities
cos(t + 2ðk) = cos t or sin(t + 2ðk) = sin t to evaluate each expression. (Enter your answers in exact form.)
(a)
sin(17ð/4)
(b)
sin(−17ð/4)
(c)
cos(17ð)
(d)
cos(45ð/4)
(e)
tan(−3ð/4)
(f)
cos(7ð/4)
(g)
sec(ð/6+2ð)
(h)
csc(2ð −ð/3)
look how I answered Kaleen's similar question
http://www.jiskha.com/display.cgi?id=1331432278
To evaluate each expression using the given identities, we can use the following steps:
(a) sin(17π/4):
We can rewrite 17π/4 as (4π + π/4). Using the identity sin(t + 2πk) = sin(t), where k is an integer, we can simplify sin(17π/4) to sin(π/4).
Therefore, sin(17π/4) = sin(π/4).
(b) sin(-17π/4):
We can rewrite -17π/4 as (-4π - π/4). Using the identity sin(t + 2πk) = sin(t), where k is an integer, we can simplify sin(-17π/4) to sin(-π/4).
Therefore, sin(-17π/4) = sin(-π/4).
(c) cos(17π):
Using the identity cos(t + 2πk) = cos(t), where k is an integer, we can simplify cos(17π) to cos(0).
Therefore, cos(17π) = cos(0).
(d) cos(45π/4):
We can rewrite 45π/4 as (8π + π/4). Using the identity cos(t + 2πk) = cos(t), where k is an integer, we can simplify cos(45π/4) to cos(π/4).
Therefore, cos(45π/4) = cos(π/4).
(e) tan(-3π/4):
We can rewrite -3π/4 as (-π/4). Using the identity tan(t + π) = tan(t), we can simplify tan(-3π/4) to tan(-π/4).
Therefore, tan(-3π/4) = tan(-π/4).
(f) cos(7π/4):
We can rewrite 7π/4 as (2π + π/4). Using the identity cos(t + 2πk) = cos(t), where k is an integer, we can simplify cos(7π/4) to cos(π/4).
Therefore, cos(7π/4) = cos(π/4).
(g) sec(π/6 + 2π):
Using the identity sec(t + 2πk) = sec(t), where k is an integer, we can simplify sec(π/6 + 2π) to sec(π/6).
Therefore, sec(π/6 + 2π) = sec(π/6).
(h) csc(2π - π/3):
Using the identity csc(t + 2πk) = csc(t), where k is an integer, we can simplify csc(2π - π/3) to csc(π/3).
Therefore, csc(2π - π/3) = csc(π/3).