Question

If cosec theta = 17/8, then find sin theta and cos theta

Answer 1

Answer:

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Answer 2

Given,

• Cosecθ = 17/8

To find,

• Sinθ
• Cosθ

Solution,

If cosecθ = 17/8, then sin theta is 8/17 cos theta is 15/17.

As we know that cosec is the reciprocal of the trigonometric function Sin, then        Sinθ =  1/Cosecθ

                       = 1/17/8

               Sinθ = 8/17

Now, Cosθ = base/ Hypotenuse

We have to find the base, that can be calculated by the Pythagoras theorem,

        $(H)^2 = (B)^2 +(P)^2$

         $(17)^2 = (B)^2 +(8)^2$

         $289 = (B)^2 + 64$

         $289-64 = (B)^2$

             $225 = (B)^2$

              $15 = B$

So, Cosθ  = 15/17

∴The value of Sinθ = 8/17 and Cosθ  = 15/17.

Hence, If cosecθ = 17/8, then sin theta is 8/17 cos theta is 15/17.