Question

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⭐ If sin A = 3/4 ........ calculate cos A and tan A

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✔❤ With explaination ❤

Answer 1

Hi.

Good Question and Keep Progressing.

Here is your answer---

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Given---
  Sin A = 3/4

For Cos A ,

  We know the Relation,
             
                   Sin^2 A + Cos^2 A = 1
 Thus,              (3/4)^2 + Cos^2 A = 1
                          Cos^A = 1 - (9/16)
                           Cos^2 A =  7/16
                            Cos A = √(7/16
                            Cos A = (√7)/4
                    
           Thus, Cos A = (√7)/4

The value of the Cos A is(√7)/4.

For tan A,

We know the relation,

              tan A = Sin A / Cos A 
             tan A  = (3/4)/({√7}/4)
             tan A  = (3/4) × (4/{√7})
             tan A   = 3/√7



Thus, the value of tan A is 3/√7.

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Hope it helps.

Have a nice day.

Answer 2

Given Sin A = 3/4.

We know that Sin^2A + cos^2A = 1

                         (3/4)^2 + cos^2A = 1

                         9/16 + cos^2A = 1

                         cos^2A = 1 - 9/16

                         cos^2A = 7/16

                         $cos A = \sqrt{ \frac{7}{16} }$

                         $cos A = \frac{ \sqrt{7} }{4}$



Now,


TanA = sinA/cosA

          $= \frac{ \frac{3}{4} }{ \frac{ \sqrt{7} }{4} }$

           $= \frac{{3} }{ \sqrt{7} }$



Hope this helps!