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if sinx = 3/5    calculate  cosx , tan, x and secx

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hadeelhadool | Student, Grade 11 | eNoter

Posted October 5, 2010 at 3:35 AM via web

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if sinx = 3/5    calculate  cosx , tan, x and secx

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted October 5, 2010 at 3:38 AM (Answer #1)

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sinx = 3/5

We know that:

sin^2 x + cos^2 x = 1

==> cosx = sqrt(1-sin^2 x)

                 = sqrt(1- 9/25)

                  = sqrt( 16/25)

                   = 4/5

==> cosx = 4/5

Now we know that:

tanx = sinx/cosx = (3/5) / (4/5) = 3/4

==> tanx = 3/4

secx = 1/cosx = 1/(4/5) = 5/4

==> secx = 5/4

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william1941 | College Teacher | Valedictorian

Posted October 5, 2010 at 3:50 AM (Answer #2)

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We know that (sin x )^2 + (cos x)^2 =1

Now sin x = 3/5

=> cos x = sqrt [ 1 - (sin x)^2]

=> cos x = sqrt [ 1 - (3/5)^2]

=> cos x = sqrt [ 1 - (9/25)]

=> cos x = sqrt ( 16 /25)

=> cos x = 4/5

tan x = sin x / cos x = (3/5) / (4/5) = 3/4

sec x = 1/ tan x = 4/3

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neela | High School Teacher | Valedictorian

Posted October 5, 2010 at 3:44 AM (Answer #3)

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Given sinx = 3/5.

cosx = sqrt(1-sin^2x) = sqrt(1-(3/5)^2) = 4/5.in tst quadrant  or -4/5 in 2nd qudrant.

secx = 1/cosx = 5/4 in 1st and -5/4 in 2nd quadrant.

tanx = sinx/cosx = (3/5)/(4/5) = 3/4 in 1st and -3/4 in 2nd quadrant.

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