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# ​ Trig Is Phun

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Hey guys im having a little trouble with trig and I would really appriciate it if someone would help me out, just answer any of them that you can help me with thanks!

Dec 8, 2017

#1
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4. sin^4(x) + sin^2(x) [cos^2(x)]  =

sin^2(x)  [   sin^2(x)  + cos^2(x) ]  =

sin^2(x) * 1

sin^2 (x)

5.  (csc x + 1) (csc x - 1)  =

csc^2 x  - 1  =

Remember that 1 + cot^2 (x) = csc^2(x)...so......subtract 1 from both sides

cot^2 x

6.    cos^2(x)  / [ 1 - sin (x) ]

Multiply top/bottom by 1 + sin (x)

cos^2(x) * (1 + sin (x)) /  [ ( 1 - sin(x))( 1 + sin (x) ]

cos^2(x)  (1 + sin (x)  / ( 1 - sin^2(x) ]

cos^2(x) (1 + sin (x) ]  / cos^2(x)

(1 + sin (x)

Dec 8, 2017
#2
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Thank you so much Cphill! Greatly appreciated!

JoeTheCat  Dec 8, 2017
#3
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2.  [  sec^2x  + csc^2x]

__________________        =

csc^2 x  [ 1 + tan^2 x]

sec^2 x                                              csc^2 x

_________________       +              ______________       =

csc^2x [ sec^2x]                           csc^2 x [ sec^2 x]

1                     +          1

___                          ______        =

csc^2 x                    sec^2 x

sin^2 x  +  cos^2 x   =

1

Dec 8, 2017
#4
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7.      1 + cos x       +      sin x

________           ______                    get a common denominator

sinx                 1 + cos x

[ 1 + cosx ] ^2 +  sin^2x

---------------------------------

sin x  [ 1 + cos x]

[ 1 + 2cosx + cos^2x] + [ 1 - cos^2 (x) ]

_________________________________

sin (x)  [1 + cos (x) ]

[    2  + 2cos^2(x) ]

_______________

sin x [ 1 + cos (x) ]

2 [  1 + cos (x) ]

______________

sin x  [ 1 + cos(x) ]

2

___            =       2csc x

sin x

I used  x instead of theta....still the same  !!!!

Dec 8, 2017
#5
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8.   tan^4x  + 2tan^2 x  +  1        factor as

[ tan^2 x + 1 ]^2   =

[sec^2( x) ]^2  =

sec^4 (x)

Dec 8, 2017
#6
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9.   sin (105)  =

sin (60+ 45)  =

sin60cos45 + sin45cos60  =

(√3/2) (√2/2)  + (√2/2)(1/2)  =

[ √6  +  √ 2 )  /  4

tan (15)  =   tan (45 - 30)  =

[ tan (45)  -  tan (30) ]            [  1  -  √3/3 ]                   3 - √ 3

_________________     =    ___________      =        _______

1  + tan (45)tan(30)                [ 1 + 1 (√3/3) ]               3  + √3

10.    sin (42°)cos(38°)  - cos(42°)sin(38°)  =

sin ( 42 - 38)   =

sin (4°)

Dec 8, 2017