Evaluate without using a calculator.
Find sin () and cos () if
tan () =
~ and sin () > 0
4
Method Method 1 tOt!
>0
Sih
>0
c= 5
~t _Il?
= _25
/6
;fc,
lCo
12
J(o ~ sec 2 e
Sine:: 3
cose;: 4
5
5
SeeS -:. .§
Ii
(5<J. vare
~
~
root boi h Sides)
cos e:: 'i
5
­
~lh
e~ i
5
1
Homework:
1,4, 9, 14,17, 25, 26, 29, 3l. 34. 37AO, 45,
47, 52,53,55,58,59,65,70,78,87
2
I do: Use basic identities to simplify the expression. cotx tan x
Ihere are
these
~hai
mCHij
\~~~~
io so Ive
problem£. .
KnoUJ ;
catx :: _,
tonx
or
catx ~ cosx
sIn x
tOhx
tanx)
I
=\
cos X
~\eihod
Meihod
,_ i. (
tonx =- sinx
=
tanx
tanx
CO$l(
Sin (x)
z
(Slnx)
·cosx
cosxslnx
-= Slnxcosx
=1
3
You do: Use basic identities to simplify the expression. tanx cos x
Hint · wherJ
tr~ 10
tan x =
s\nx
cosx
problem£,
Slmpllf~ ~rob\etn~ 10 Sin X~ COSX.
c\O\\\g
-These-
SIIIK -r
coS' X
-=
cosx
4
I do: Simplify the expression to either 1 or -1. Sl(\~
(s C (-X)::
cseC-x)
(sex
- Cs ex
= _I SIf\)< ~Inx ( ~):= -1
Slnx
~:
51nx
cosx
tanx Stcx csex
rewr, te ; 5\n x esc x cos x secx
'\
t
Inverses
:=
tonx
'J'
I(
InverS~5
1
::
'=
I
tanx
5
You do:
Use basic identities to simplify the expression.
Sln 2
e=
Sine
Sin
e
6
You do: How was this equation simplified? sec 2 x - tan 2 x
2
2
COS U + sin u
1
=
to n2 e t I ::: se c Z G
~
I
~----
"j:j: 25 '
~
2
(sec x
t
CSc 2 X) -
b seClX
I
(ron 2 x
t cSe 2l(
sec 2x - tQ\1 2x
I::: Se (2 G - to h
t
::
z. e
{
iCOt 2 ><)
-tonlx - co"F x
csc 2x - cot 2x
~~
I
7
We do:
Write each expression in factored form as an algebraic
expression of a single trig function.
4 tan 2 x - -
4
cotx
* 1'10 Ke
e-ver~ih\rl9
Lei
Sll\xcscx ~ SillX' (~ ) :::.
iUrlX
1ton 2x - 4tanx
+ sin x esc x
Sln)(
+
tanx = X
4x z yX
(2X --::
I )
+j
(2x
(Zx _I)
( 2tonx
I) 2
-I) 2
8
Solve the assigned problem.
Write the solution on the yellow paper.
-J2 tah)(
'-
cOSX - tOrlX =
~
0
..J
fut In y,
-t Change
-Y Flhd
WlhdotJJ
~\jhe re
to
j
I
::
0
x=o, 3.J4, 5.5
l.7T
,
t
I
I
,~
9