Download Pre-Calculus - Shelbyville CUSD #4

Pre-Calculus
Section 6.1
Using Fundamental Identities
Review identities on p. 498.
Use the given values to evaluate (if possible) the remaining
trigonometric functions.
1.
sin x  1 , cos x  3
2
2
2.
tan x  7 , sec x   25
24
24
3.
tan x = 2, sin x < 0
4.
sin   x    2 , tan x   2 5
5
3
Match the trigonometric expression with one of the following.
(a) –tan x
(e) -1
(b) tan x
(f) sec2x
1.
secx cosx
2.
cot2x – csc2x
3.
sin   x 
cos   x 
4.
sinx secx
5.
sec4x – tan4x
6.
sec2 x 1
sin 2 x
(c) 1
(d) sec2 x + tan2 x
Use the fundamental identities to simplify the expression. Use the table
feature of a graphing calculator to check your result numerically.
1.
cotx sinx
2.
sinφ(cscφ – sinφ)
3.
csc x
cot x
Verify the identity algebraically.
1.
sin x + cos x cot x = csc x
2.
1 cos  sin  2csc
1 cos
sin
3.
csc x tan x = sec x
4.
cot( )
  cos
csc
Factor the expression and use the fundamental identities to simplify.
1.
cot2 x – cot2 x cos2 x
3.
sin4x – cos4x
2.
tan4 x + 2tan2 x + 1
Perform the indicated operations and use the fundamental identities to
simplify.
1.
(sin x + cos x)2
2.
(csc x + 1)(csc x – 1)
3.
1  1
1 cos x 1 cos x
4.
2
tan x  sec x
tan x
Rewrite the expression so that it is not in fractional form.
1.
sin 2 
1 cos
HW: p. 503-504 2-72 even
2.
3
sec x  tan x