Question

if tan theta equal to 8 by 15 find the values of their trigonometrical ratios for teta ​

Answer 1

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➠ If tanθ = 8/15 find the values of their trigonometric ratios for "θ" .

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❏ Trigonometry is one of the most important topic in modern mathematics that is useful in various field.

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❏ Here are the simple formula to find various trigonometric ratios if 2 sides of triangle is known.

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$\boxed { \bold { :\leadsto \; sin\theta = \dfrac{Opposite \; side}{ Hypotenuse} } }$

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$\boxed { \bold { :\leadsto \; cos\theta = \dfrac{Adjacent \; side}{ Hypotenuse} } }$

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$\boxed { \bold { :\leadsto \; tan\theta = \dfrac{Opposite \; side}{ Adjacent \; side} } }$

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$\boxed { \bold { :\leadsto \; cosec\theta = \dfrac{ Hypotenuse}{Opposite \; side} } }$

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$\boxed { \bold { :\leadsto \; sec\theta = \dfrac{ Hypotenuse}{Adjacent \; side} } }$

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$\boxed { \bold { :\leadsto \; cot\theta = \dfrac{ Adjacent \; side}{Opposite \; side} } }$

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➠ If tanθ = 8/15

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Let's Start !

   

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Let's assume the following triangle in given attachment !

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As tanθ = 8/15,

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AB = 15k

BC = 8k

AC = ?

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By Pythagoras theorem ,

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$\bold { \red { :\implies AB^2 + BC^2 = AC^2 } }$

$\bold { \blue { :\implies (8k)^2 + (15k)^2 = AC^2 } }$

$\bold { \green { :\implies 64k^2 + 225k^2 = AC^2 } }$

$\bold { \blue { :\implies AC^2 = 289k^2 } }$

$\boxed { \bold { \orange { :\implies AC = 17k } } }$

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Now by finding hypotenuse we can calculate trigonometric ratios !

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• Opposite side = BC = 8k
• Adjacent side = AB = 15k
• Hypotenuse = AC = 17k

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$\bold { :\leadsto \; sin\theta = \dfrac{Opposite \; side}{ Hypotenuse} = \dfrac{8k}{ 17k} = \dfrac{8}{17} }$

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$\bold { :\leadsto \; cos\theta = \dfrac{Adjacent \; side}{ Hypotenuse} = \dfrac{15k}{ 17k} = \dfrac{15}{17} }$

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$\bold { :\leadsto \; tan\theta = \dfrac{Opposite \; side}{ Adjacent \; side} = \dfrac{8k}{ 15k} = \dfrac{8}{15} }$

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$\bold { :\leadsto \; cosec\theta = \dfrac{ Hypotenuse}{Opposite \; side} = \dfrac{ 17k}{8k} = \dfrac{17}{8} }$

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$\bold { :\leadsto \; sec\theta = \dfrac{ Hypotenuse}{Adjacent \; side} = \dfrac{ 17k}{15k} = \dfrac{17}{15} }$

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$\bold { :\leadsto \; cot\theta = \dfrac{ Adjacent \; side}{Opposite \; side} = \dfrac{ 15k}{8k} = \dfrac{15}{8} }$

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Hereby we are done with all trigonometric ratios .-.

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Hope this helps u.../

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