MATH 108 Fall 2013 HW 2

DesertSimplify the expression completely.

 

1)

=21*cos^(3)x*(sinx)/(7*sinx*sinx*cosx)

 

21*cos^(3)x*(sinx)/(7sinx*sinx*cosx)

 

21*cos^(3)x*(sinx)/(7sin^(2)x*cosx)

 

21*cos^(3)x*(sinx)/(7cosxsin^(2)x)

 

21*cos^(3)x*(1)/(7sinxcosx)

 

21*cos^(3)x*(1)/(7cosxsinx)

 

21*cos^(2)x*(1)/(7sinx)

 

21cos^(2)x*(1)/(7sinx)

 

(21cos^(2)x)/(7sinx)

 

(3cos^(2)x)/(sinx)

 

3cosxcotx

 

2)        = 1/ (cosx+sinx) * [4/(sinx+cosx)+7]= 1/ (cosx+sinx) * [4+sinx+cosx]  =  1/(cos^2x – sin^2x) (4 + 7 sinx + 7cosx)

 

3)  = 10 / 5  *  tan^3x/tanx *  sec^2x / sec x = 2 * tan^2x *secx

 

4) =  (cos^2x – 2 cosx  – 8 ) / (cosx -4) = cos^2x – 2cosx +1  – 9  = (cosx-1)^2  – 3 ^2  /(cosx-4) =( cos x +2)

 

 

Find the exact circular function value.

5) cos 2π/3 = cos (Π -Π/3) = -cos 60 = -.5

 

6) tan 5π/6 = tan (Π –Π/6) = – cot 30 = -.577.

 

Graph.

7) y = sin(x + 3π/2)

 

 

Find the amplitude, period or phase shift.

8) Find the period and phase shift of y =

y=Acos(Bx-C), A=amplitude, Period=2π/B, Phase Shift=C/B

period = 2 * π / ¼ = 8 / π.

 

9) Find the amplitude of y = 5 cos (x – π).

Amplitude a = 5.

y=Asin(Bx-C), A=amplitude, Period=2π/B, Phase Shift=C/B

 

10) Find the period of y = 2 cos (2x + π/3).

Period = 2 * π / 2 = π.
11) Find the phase shift of y = -4 + 3sin (5x – π/6)

Phase shift =  π/6 /5  = π/30.

 

Find the trigonometric function value of angle θ.

12)  sin θ = – 5/13 and θ in quadrant III

Find sec θ and csc θ

 

Cos @ = sqrt (1 – (5/13)^2) = 12/13

Sec @ = 13/12

Cosec @= -13/5.

 

13) cot θ = – ¾ and θ in quadrant II

Find csc θ and sinθ

 

Cosec^2 @ = 1 + 9/16 = 25/16

Cosec @ = 5/4

Sin @=  4/5.

 

 

15) Find  exactly in degrees. = 210 degree

 

16) Find  exactly in radians. = Π/3.

 

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