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Algebraic Trig Worksheet 1) Simplify the Following: a) 1 csc x cos x cot x ( ) 2 cos x b) csc x sin x 1 cot x sin x cos 2 x 1 c) 3 3 csc 2 x 2 sec 2 x 1 + cos 1 + sec 2 d) cot 2 x 1 tan 2 x 1 csc x tan x cos x csc x csc x 1 sec 2 x e) cos x sin 3 x + sin 3 x cos x sin x + 2 tan x csc x sec x cot x sin x + sin x cos x sec 2 x 1 cos 2 x

7.1 and 7.2 Worksheet - Southern Oregon Universitywebpages.sou.edu/~stonelakb/math/pdf/7.1 and 7.2 Worksheet solut… · 7.1 and 7.2 Worksheet Author: Brian Stonelake Created Date:

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Page 1: 7.1 and 7.2 Worksheet - Southern Oregon Universitywebpages.sou.edu/~stonelakb/math/pdf/7.1 and 7.2 Worksheet solut… · 7.1 and 7.2 Worksheet Author: Brian Stonelake Created Date:

Algebraic*Trig*Worksheet**1) Simplify*the*Following:*

a) 1− csc x − cos x ⋅cot x( )2cos x

*

**

***

b) *−

csc xsin x

−1

cot x ⋅sin xcos2 x −1

*** *

**

***

c) 3− 3csc2 x

− 2sec2 x

1+ cos1+ sec

⎛⎝⎜

⎞⎠⎟2 **

******

d) −cot2 x − 1tan2 x

⎛⎝⎜

⎞⎠⎟

1csc x

− tan xcos x

csc x − csc x ⋅ 1sec2 x

⎜⎜⎜

⎟⎟⎟**

******

e) cos x sin3 x + sin3 xcos x ⋅sin x

+

2tan x

⋅ csc xsec x

cot xsin x

+ sin x ⋅cos x ⋅sec2 x

1− cos2 x

⎜⎜⎜

⎟⎟⎟**

** *

Page 2: 7.1 and 7.2 Worksheet - Southern Oregon Universitywebpages.sou.edu/~stonelakb/math/pdf/7.1 and 7.2 Worksheet solut… · 7.1 and 7.2 Worksheet Author: Brian Stonelake Created Date:

2) sin 18!( ) = 5 −1

4.*Find* sin 78! .**

Hint:* sin(A + B) = sinAcosB + cosAsinB **

*******3) Evaluate* cos arcsin 3

5 − arctan 512( ) .*

*Hint:* cos(A − B) = cosAcosB + sinAsinB ********

*4) Evaluate* tan arcsin x + arctan y( ) .**

Hint:* tan(A + B) = tanA + tanB1− tanA tanB

**

**********

5) Earlier*in*the*term,*there*was*a*HW*question*that*was*impossible*without*the*double*angle*formula.*I*told*you*to*just*assume*that* sin 2x( ) = 2sin xcos x .*Prove*this*fact*using*an*angle*addition*formula.**

*