Question

If Cos θ = 35/37 , then what is the value of Cot θ?

A) 12/35 B) 35/12 C) 37/12 D) 12/37

Answer 1

Answer:

Answer is option B. Cotθ= 35/12

Step-by-step explanation:

GIVEN:

• Cosθ=35/37

• Using trigonometric identities,

                                    $1. \frac{Sin\theta}{Cos\theta} = Tan\theta\\\\2. tanx^{-1}\theta=cot\theta\\ \\3. cot\theta=\frac{Cos\theta}{Sin\theta}$

                                    $4. Sin^{2}\theta+ Cos^{2} \theta=1$

• $&\sin ^{2} \theta=1-\cos ^{2} \theta$

                 $=1-(35 / 37)^{2}$

                 $=144 / 1369$

         $\sin \theta=\sqrt{ \frac{144}{1369} }=12 / 37$

Therefore,

$\cot \theta=\cos \theta / \sin \theta$

        $=\frac{35/37}{12/37} \\=\frac{35}{12}$

Answer 2

Answer:

$COT$θ =$\frac{35}{12}$

Step-by-step explanation:

TO FIND: COTθ =?

GIVEN : COSθ=$\frac{35}{37}$

FROM Trignometry identites

   $SIN^{2}$θ +$COS^{2}$θ=$1$

   $SIN^{2}$θ=$1-COS^{2}$θ

  $SIN^{2}$θ=$1-(\frac{35}{37})^{2}$

   $SIN^{2}$θ=$\frac{144}{1369}$

   $SIN$θ=$\sqrt{\frac{144}{1369} }$

  $SIN$θ=$\frac{12}{37}$

COTθ=COS θ / SINθ

       =   $\frac{\frac{35}{37} }{\frac{12}{37} }$

  COTθ=$\frac{35}{12}$

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