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Q.




If sinA= 3 4  ,what is the value of cos A?

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a

5 4  

b

7 8  

c

7 4  

d

5 8     

answer is C.

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Detailed Solution

Given that sinA= 3 4  .
we know that the sine of an angle is defined as,
sinθ= Perpendicular Hypotenuse  
Let hypotenuse be 4k and perpendicular be 3k for some constant k.
We know that according to Pythagoras theorem,
Hypotenus e 2 =Bas e 2 +Perpendicula r 2  .
Putting the values of B and H,
B 2 = 16 k 2 −9 k 2 B= 7 k 2 B=k 7  
Now we know that,
cosθ= Base Hypotenuse  
here  B = 7  k and H = 13k.
⇒tanθ= 7 k 4k ⇒tanθ= 7 4  
Therefore, the correct option is 3.
 
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