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if 3sinß + 4cosß = 5, find the value of tanß

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rnk | Student, Grade 10 | Honors

Posted October 18, 2011 at 4:54 PM via web

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if 3sinß + 4cosß = 5, find the value of tanß

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

Posted October 19, 2011 at 10:21 AM (Answer #1)

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`3sinbeta + 4cosbeta = 5`

`sin^2 beta + cos^2 beta = 1`

`==> cosbeta = sqrt(1-sin^2 beta)`

`==> 3sinbeta + 4sqrt(1-sin^2 beta) = 5`

`==> 3sinbeta -5 = 4sqrt(1-sin^2 beta)`

`==. 9sin^2 beta -30sinbeta +25 = 16(1-sin^2 beta)`

`==> 9sin^2 beta -30sinbeta +25 = 16 - 16sin^2 beta`

`==> 25sin^2 beta -30sinbeta +9 = 0`

`==> (5sinbeta +3)^2 = 0`

`==> sinbeta = -3/5`

`==>beta = -36.8699`

`==> tanbeta = tan(-36.8699) =-0.75 = -3/4`

`==> tanbeta = -3/4`

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