Let x be an angle in quadrant III such that sin(x)= -7/8. Find the exact values of sec(x) and tan(x).

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The angle x is in the third quadrant where the value of cos x is negative.

`sin x = -7/8`

`cos x = -sqrt(1 - (-7/8)^2)`

=> `-sqrt((64 - 49)/64)`

=> `-sqrt 15/8`

sec x = `1/cos x` =` -8/sqrt 15`

`tan x = sin x/cos x = (-7/8)/(-sqrt 15/8)`

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The angle x is in the third quadrant where the value of cos x is negative.

`sin x = -7/8`

`cos x = -sqrt(1 - (-7/8)^2)`

=> `-sqrt((64 - 49)/64)`

=> `-sqrt 15/8`

sec x = `1/cos x` =` -8/sqrt 15`

`tan x = sin x/cos x = (-7/8)/(-sqrt 15/8)`

=> `7/sqrt 15`

The value of sec x = `-8/sqrt 15` and tan x = `7/sqrt 15`

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