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 at my answer to Kaleen
http://www.jiskha.com/display.cgi?id=1331432278
the questions are similar.
To evaluate each expression using the given identities, we will substitute the angle in the identity and simplify it.
(a) sin(17ð/4):
Using the identity sin(t + 2ðk) = sin(t), we can rewrite sin(17ð/4) as sin(ð/4).
(b) sin(-17ð/4):
Using the identity sin(t + 2ðk) = sin(t), we can rewrite sin(-17ð/4) as sin(ð/4).
(c) cos(17ð):
Using the identity cos(t + 2ðk) = cos(t), we can rewrite cos(17ð) as cos(0).
(d) cos(45ð/4):
Using the identity cos(t + 2ðk) = cos(t), we can rewrite cos(45ð/4) as cos(ð/4).
(e) tan(-3ð/4):
Using the identity tan(t + 2ðk) = tan(t), we can rewrite tan(-3ð/4) as tan(ð/4).
(f) cos(7ð/4):
Using the identity cos(t + 2ðk) = cos(t), we can rewrite cos(7ð/4) as cos(ð/4).
(g) sec(ð/6 + 2ð):
Using the identity sec(t + 2ðk) = sec(t), we can rewrite sec(ð/6 + 2ð) as sec(ð/6).
(h) csc(2ð - ð/3):
Using the identity csc(t + 2ðk) = csc(t), we can rewrite csc(2ð - ð/3) as csc(ð/3).
Now, you can simplify each expression individually using any trigonometric functions or formulas you are familiar with.