Your Federal Quarterly Tax Payments are due April 15th

# TRIG – Chapter 5 – Identities by malj

VIEWS: 15 PAGES: 3

• pg 1
```									                                  MAC 1114 - TRIG –5.2a

A. Complete the right side using the indicated identity
I. Reciprocal Identities

sin  =            cos  =                       sec  =

csc  =            tan  =                       cot  =

II. Quotient Identities

tan  =                                cot  =

III. Pythagorean Identities and the alternate versions of each

cos2  + sin2  =

1 + tan2  =

cot2  + 1 =

IV. Co-function Identities

sin  =                      cos  =                          tan  =

V. Negative Angle Identities

sin ( -  ) =               cos ( -  ) =                    tan ( -  ) =
B. Match the expression on the left with an equivalent expression on the right.
(Taken from page 187 problems 29 – 33 in the text)

Column I                           Column II

cos x
1.                                 (a) sin2 x + cos2 x
sin x

2. tan x                           (b) cot x

3. cos ( - x )                     (c) sec2 x

sin x
4. tan2 x + 1                      (d)
cos x

5. 1                                (e) cos x

C. Simplify the left side using properties of algebra (if possible).
6. sin x + sin x =                            7. sin x – sin x =

sin x
8. sin x  sin x =                            9.         =
sin x

10. sin x + sin y =                           11. sin x ( 1 + sin x ) =

sin 2 x
12.            =
sin x
D. Use properties of Algebra and substitutions based on Trig Identities to perform
should not contain parentheses or fractions.
cos 2 x sin 2 x                                 cos x sin x
13.                                            14.       
3       3                                     sin x cos x

1     sin x                                             1       sin x
15.                                                     16.            
sin x 1  cos x                                       1  cos x 1  cos x

17.   ( 1 + tan x )2 – 2 tan x

Simplify each expression to a constant, a single trig function or a power of a function.
sin 2 x
18.        2
19. cot x tan2 x
cos x

1
20.     cot x sin x                                      21..             cot x tan x
tan 2 x

E. Match the expression on the left with an equivalent expression on the right.
Column I                               Column II

sin 2 x
22. -tan x cos x                             (a)
cos 2 x

1
23. sec2 x – 1                               (b)
sec2 x

sec x
24.                                          (c) sin ( - x )
csc x

25. 1 + sin2 x                               (d) csc2 x – cot2 x + sin2 x

26. cos2 x                                    (e) tan x

```
To top