Question

if sec theta = 5/3 and 0< theta <π/2. find all the T-ratios​

Answer 1

Answer:

cos theta=3/5. (sec theta=1/cos theta)

sin^2theta=1-cos^2theta

1-9/25

16/25

sin theta=4/5

tan theta=sin theta/cos theta

4/5/3/5=4/3

cot theta=3/4. (1/tan theta)

cosec theta=5/4. (1/sin theta)

Answer 2

Answer:

When sec theta = 5/3, By Pythagoras theorem  the remaining  trigonometric ratios are listed below,

             sin theta = opposite/hypotenuse   = 4/5

            cos theta = adjacent/hypotenuse   = 3/5

             tan theta = opposite/adjacent        = 4/3

         cosec theta = hypotenuse/opposite  = 5/4

              cot theta = adjacent/opposite        = 3/4

Explanation:

Trigonometric Ratio:

• Based on the right angled triangle we have total 6 trigonometric ratios, which are  given below

            sin theta = opposite/hypotenuse    

            cos theta = adjacent/hypotenuse  

             tan theta = opposite/adjacent      

         cosec theta = hypotenuse/opposite

             sec theta = hypotenuse/adjacent

              cot theta = adjacent/opposite  

• Given,

              sec theta = 5/3   then

              cos theta = 3/5     since {cos theta = 1/(sec theta)}

           So, here adjacent value = 3, hypotenuse value = 5

• To find the value of adjacent, we apply Pythagoras theorem

             By Pythagoras theorem,

                    $(hypotenuse)^{2} = (opposite)^{2} +(adjacent)^{2}$

                Let opposite value = x

             By Pythagoras theorem we can write,

                        $5^{2}=x^{2} +3^{2}$

                        $x^{2}=5^{2}-3^{2}$

                        $x=\sqrt{25-9}$

                         $x=\sqrt{16}$

                         $x=4$

            Hence, opposite value = 4

       By the values

            adjacent value = 3, opposite value = 4, hypotenuse value = 5

       Now all the trigonometric ratios can be written as

             sin theta = opposite/hypotenuse   = 4/5

            cos theta = adjacent/hypotenuse   = 3/5

             tan theta = opposite/adjacent        = 4/3

         cosec theta = hypotenuse/opposite  = 5/4

              cot theta = adjacent/opposite        = 3/4

               

Learn more about  Trigonometry:

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