Can some one help me plzzz will give brainiest
1 answer:
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Answer:
y = 2 sin (x + ) has the same graph of y = 2 cos (x +
) ⇒ 3rd answer
Step-by-step explanation:
Let us revise the rules of the trigonometric compound angles
cos(x + y) = cos x cos y - sin x sin y
sin(x + y) = sin x cos y + cos x sin y
Let us solve the problem using the rules above
y = 2 cos (x + )
∵ 2 cos (x + ) = 2[cos x cos
- sin x sin
]
∵ cos =
and sin
=
- Substitute them in the right hand side
∴ 2 cos (x + ) = 2[
cos x -
sin x]
- Multiply the bracket in the right hand side by 2
∴ 2 cos (x + ) =
cos x -
sin x
∴ y = cos x -
sin x
Now let us find the function which give the same right hand side of the function above
y = 2 sin (x + )
∵ 2 sin (x + ) = 2[sin x cos
+ cos x sin
]
∵ sin =
and cos
=
- Substitute them in the right hand side
∴ 2 sin (x + ) = 2[
sin x +
cos x]
- Multiply the bracket in the right hand side by 2
∴ 2 sin (x + ) =
sin x +
cos x
- Switch the two terms of the right hand side
∴ 2 sin (x + ) =
cos x -
sin x
∴ y = cos x -
sin x
- The same with right hand side of the function above
∴ y = 2 sin (x + ) has the same graph of y = 2 cos (x +
)