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If 8 sin x = 4 + cos x, the values of sin x are a. 3/5, -5/13 b.-3/5, -5/13 c. 3/5,...

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madmoni06 | Student | (Level 1) Honors

Posted April 3, 2013 at 12:00 PM via web

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If 8 sin x = 4 + cos x, the values of sin x are

a. 3/5, -5/13

b.-3/5, -5/13

c. 3/5, 5/13

d. 5/18, 5/3

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durbanville | High School Teacher | (Level 1) Educator Emeritus

Posted April 3, 2013 at 12:44 PM (Answer #2)

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Please note that the answer should be c) `3/5 ; 5/13`

8sinx=4+cosx

8sinx-4=cosx

Follow the same procedure as above by squaring both sides:

`(8sin x -4)^2 = cos^2x`

`64 sin^2x - 64 sin x +16 = cos^2x`

`cos^2x= 1-sin^2 x`  (identities)

Take the `1-sin^2x` over to the other side:

`65 sin^2x - 64 sinx +15 = 0`

Factorize using the factors of 65 (1 x65; 5 x 13) and 15(1x15; 3 x 5) which work (5 x 13 and 3 x 5):

`(13 sin x - 5)(5sin x -3) = 0`

This combination will render a middle term of - 64 (negative) and +15 at the end

`therefore 13sinx = 5`    and `5sinx = 3`

`therefore sinx=5/13`         and `sin x = 3/5`

Answer: c

 

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