SOLUTION: Using the pythagorean identities, if sin^2 is 4/7, then what is tan^2

Question 858308: Using the pythagorean identities, if sin^2 is 4/7, then what is tan^2
Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!

Hi, there--

Problem:
Using Pythagorean Identities, is , then what is ?

Solution:
We have three forms of the Pythagorean Identity:
I. 
II. 
III. 

We will make a series of substitutions in order to get  in terms of .

Rearrange Identity I,


If a = b, then 1/a=1/b. So


By definition, 1/cos(x)=sec(x). So,


By Identity II, substitute  for 


Subtract 1 from both sides to isolate  on the left side.


Substitute 4/7 for .


Simplify.



Why can CHECK OUR ANSWER using Identity I and the definition of tangent.



Substitute 4/7 for  and simplify.



By definition tan(x) = sin(x) / cos(x). So,


Substitute 4/7 for  and 3/7 for .


Simplify.


I hope this helps. Feel free to email me if you have any questions about these steps.

Mrs. Figgy
math.in.the.vortex@gmail.com

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