Question

If cot theta is equal to 2 find the value of all trigonometry ratios of theta​

Answer 1

$\Large{\underline{\underline{\mathfrak{\bf{Question}}}}}$

If cot theta is equal to 2 find the value of all trigonometry ratios of theta .

$\Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}$

$\Large{\underline{\mathfrak{\bf{Given}}}}$

• $\sf{\:\cot \theta\:=\:\dfrac{2}{1}}$

$\Large{\underline{\mathfrak{\bf{Find}}}}$

• The value of all trigonometry ratios of theta .

$\Large{\underline{\underline{\mathfrak{\bf{Explanation}}}}}$

We know,

$\boxed{\small{\sf{\pink{\:\cot \theta\:=\:\dfrac{Base}{perpendicular}}}}}$

In, A/c to this Attachment

$\boxed{\small{\sf{\pink{\:Hypotenuse\:=\:\sqrt{(Base)^2+(perpendicular)^2}}}}} \\ \\ \mapsto\sf{\:Hypetenuse\:=\:\sqrt{(2)^2+(1)^2}} \\ \\ \mapsto\sf{\:Hypotenuse\:=\:\sqrt{4+1}} \\ \\ \mapsto\sf{\orange{\:Hypotenuse(AC)\:=\:\sqrt{5}}}$

Now, calculate other trigonometry ratio , and a/c to attachment

First:-

$\boxed{\small{\sf{\pink{\:\sin \theta\:=\:\dfrac{perpendicular}{hypotenuse}\:=\:\dfrac{AB}{AC}}}}} \\ \\ \mapsto\sf{\:\sin \theta\:=\:\dfrac{1}{\sqrt{5}}\:\:\:\:\:Ans.}$

Second:-

$\boxed{\small{\sf{\pink{\:\cos \theta\:=\:\dfrac{base}{hypotenuse}\:=\:\dfrac{BC}{AC}}}}} \\ \\ \mapsto\sf{\:\cos \theta\:=\:\dfrac{2}{\sqrt{5}}\:\:\:\:\:Ans.}$

Third:-

$\boxed{\small{\sf{\pink{\:\tan \theta\:=\:\dfrac{perpendicular}{base}\:=\:\dfrac{AB}{BC}}}}} \\ \\ \mapsto\sf{\:\tan \theta\:=\:\dfrac{1}{2}\:\:\:\:\:Ans.}$

Fourth:-

$\boxed{\small{\sf{\pink{\:\sec \theta\:=\:\dfrac{hypotenuse}{base}\:=\:\dfrac{AC}{BC}}}}} \\ \\ \mapsto\sf{\:\sec \theta\:=\:\dfrac{\sqrt{5}}{2}\:\:\:\:\:Ans.}$

Fifth:-.

$\boxed{\small{\sf{\pink{\:\cosec \theta\:=\:\dfrac{hypotenuse}{perpendicular}\:=\:\dfrac{AC}{AB}}}}} \\ \\ \mapsto\sf{\:\cosec \theta\:=\:\dfrac{\sqrt{5}}{1}\:\:\:\:\:Ans.}$

Answer 2

$\:$

Statement:

If cot theta = 2 then find all the trigonometry ratios of theta

Then by Pythagoras theorem

AB^2 + BC^2 = AC^2

1^2+ 2^2 =AC^2

1+4=AC^2

5=AC^2

√5=AC

Therefore the values of all the trigonometric ratios are =

Sin theta=1/√5

Cos theta=2/√5

Tan theta=1/2

Cosec theta=√5/1

Sec theta=√5/2