State-the-phase-shift-the-amplitude-and-draw-the-graph-a-g-3-4-sin-2-pi-b-f-1-3-4-sin-2-pi-c-f-4-

Question Number 42036 by Tawa1 last updated on 17/Aug/18

State the phase shift, the amplitude and draw the graph .

(a) g (θ) = \frac{3}{4} \sin (2 θ + π)

(b) f (θ) = 1 + \frac{3}{4} \sin (2 θ + π)

(c) f (θ) = 4 θ

Commented by maxmathsup by imad last updated on 17/Aug/18

a) g (θ) = - \frac{3}{4} s i n (2 θ) w e h a v e g (θ + π) = - \frac{3}{4} s i n (2 (θ + π))

= - \frac{3}{4} s i n (2 θ + 2 π) = - \frac{3}{4} s i n (2 θ) = g (θ) \Rightarrow g p e r i o d i c w i t h T = π

w e c a n s t u d y t h e v a r i a t i o n o n [- \frac{π}{2}, \frac{π}{2}] b u t g (- θ) = \frac{3}{4} s i n (2 θ) = - g (θ) \Rightarrow

g i s o d d s o w e c a n s t u d y t h e v a r i a t i o n o n [0, \frac{π}{2}] = [0, \frac{π}{4}] \cup [\frac{π}{4}, \frac{π}{2}]

g^{^{'}} (θ) = - \frac{3}{2} c o s (2 θ) w e h a v e 2 θ \in [0, π]

x 0 \frac{π}{4} \frac{π}{2} w e h a v e g (o) = 0, g (\frac{π}{4}) = - \frac{3}{4}

g^{^{'}} (x) - + g (\frac{π}{2}) = 0 \dots .

g (x) d e c r i n c

Commented by tanmay.chaudhury50@gmail.com last updated on 17/Aug/18

s t e p s t o d r a w \dots

1) d r a w s i n θ i n b e t w e e n θ = 0 a n d 2 Π \dots w e k n o w

t h e s h a p e o f s i n θ t h e n r e p e a t e t h e s h a p e b u t

- v e s i d e . .

2) f (θ) 0 30^{o} 45^{o} 60^{o} 90^{o} 120^{o} 135^{o} 150^{o} 180^{o}

s i n θ 0 \frac{1}{2} \frac{1}{\sqrt{2}} \frac{\sqrt{3}}{2} 1 \frac{\sqrt{3}}{2} \frac{1}{\sqrt{2}} \frac{1}{2} 0

n o w i a t t a c h i n g t o c l a r i f y \dots

Commented by tanmay.chaudhury50@gmail.com last updated on 17/Aug/18

Commented by tanmay.chaudhury50@gmail.com last updated on 17/Aug/18

Commented by tanmay.chaudhury50@gmail.com last updated on 17/Aug/18

Commented by tanmay.chaudhury50@gmail.com last updated on 17/Aug/18

Commented by tanmay.chaudhury50@gmail.com last updated on 17/Aug/18

Commented by Tawa1 last updated on 17/Aug/18

God bless you sir

Commented by Tawa1 last updated on 17/Aug/18

God bless you sir

Commented by Tawa1 last updated on 17/Aug/18

I appreciate your effort

Commented by tanmay.chaudhury50@gmail.com last updated on 17/Aug/18

i f y o u w a n t f r e e b o o k s p d f f o r m d o w n l o a d a b l e

s e a c h a r c h i v e s . o r g t h e n i n s e a r c h o p t i o n w r i t e

p h y s i c s o r m a t h e m a t i c s o r g r a p h o r a l g e b r a

h e r e y o u g e t i r o d o v k r o t o v s l l o n e h

a l g e b r a h a l l a n d k n i g h t e t c \dots

Commented by Tawa1 last updated on 17/Aug/18

Wow, i will try it sir . God bless you sir

Commented by Tawa1 last updated on 17/Aug/18

It is good sir . thanks . God bless you

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