Question

if tan theta =2 then find all other trigonometric ratios​

Answer 1

Answer:

Here tan theta=2/1

so hypotenuse =√(2)^2 + (1)^2 = √5.

sin theta = opposite side /hypotenuse = 2/√5. cosec theta = 1/sin theta = √5/2

Cos theta = adjacent side / hypotenuse = 1/√5. sec theta =1/cos theta = √5/1 =√5

tan theta = opposite side/ adjacent side =2/1. cot theta =1/tan theta = 1/2

HOPE IT HELPS U

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Answer 2

$\huge\frak{\underline{\underline{\pink{\:QUESTION}}}}$

if tan theta =2 then find all other trigonometric ratios .

$\huge\frak{\underline{\underline{\pink{\:ANSWER}}}}$

$\large{\sf{\underline{\:GIVEN}}}$

$\mapsto\red{\sf{\:\tan \theta\:=\:2}}$

$\large{\sf{\underline{\:FIND}}}$

$\mapsto\red{\sf{\:All\:Trigonometric\:ratio}}$

$\huge\frak{\underline{\underline{\pink{\:Explanation}}}}$

We Have,

A/C to Picture.

$\underline{\green{\sf{\:(In\:\triangle\:ABC)}}}$

$\:\:\:\:\small{\pink{\sf{\:(By\:Pythagoras\:theorem)}}}$

$\:\:\:\:\large\green{\sf{\:(AC)^2\:=\:(AB)^2+(BC)^2}}$

$\mapsto\sf{\:(AC)^2\:=\:(2)^2+(1)^2}$

$\mapsto\sf{\:(AC)^2\:=\:4+1}$

$\mapsto\sf{\:(AC)\:=\sqrt{5}}$

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Now, Calculate

$\large\boxed{\boxed{\green{\sf{\:\left(\sin \theta\:=\dfrac{(Perpendicular)}{(Hypotenuse)}\right)}}}}$

$\mapsto\large\pink{\sf{\:\left(\sin \theta\:=\dfrac{2}{\sqrt{5}}\right)}}$

$\large\boxed{\boxed{\green{\sf{\:\left(\cos \theta\:=\dfrac{(Base)}{(Hypotenuse)}\right)}}}}$

$\mapsto\large\pink{\sf{\:\left(\cos \theta\:=\dfrac{1}{\sqrt{5}}\right)}}$

$\large\boxed{\boxed{\green{\sf{\:\left)\cot \theta\:=\dfrac{(Base)}{(Perpendicular )}\right)}}}}$

$\mapsto\large\pink{\sf{\:\left(\cot \theta\:=\dfrac{1}{2}\right)}}$

$\large\boxed{\boxed{\green{\sf{\:\left(\sec \theta\:=\dfrac{(Hypotenuse)}{(Base)}\right)}}}}$

$\mapsto\large\pink{\sf{\:\left(\sec \theta\:=\dfrac{\sqrt{5}}{1}\right)}}$

$\large\boxed{\boxed{\green{\sf{\:\left(\cosec \theta\:=\dfrac{(Hypotenuse)}{(Perpendicular)}\right)}}}}$

$\mapsto\large\pink{\sf{\:\left((\cosec \theta\:=\dfrac{\sqrt{5}}{2}\right)}}$

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