Question

Given sin A =11\61 and that angle A is in Quadrant I find the exact value of tan A in simplest radical form using a rational denominator

Answer 1

Answer:

Therefore,

$\tan A=\dfrac{11}{60}$

Step-by-step explanation:

Given:

$\sin A=\dfrac{11}{61}$

A is in I Quadrant

To Find:

$\tan A = ?$

Solution:

Using Identity

$\sin^{2}A+\cos^{2}A=1$

Now Substitute Sin A we get

$(\dfrac{11}{61})^{2}+\cos^{2}A=1\\\\\cos^{2}A=1-\dfrac{121}{3721}=\dfrac{3600}{3721}\\\\\cos A=\pm\sqrt{\dfrac{3600}{3721}}\\\\\cos A=\dfrac{60}{61}$

As 'A' is in First Quadrant Cos A is Positive

Now Tan identity we have

$\tan A=\dfrac{\sin A}{\cos A}$

Now Substitute Sin A and Cos A  we get

$\tan A=\dfrac{\dfrac{11}{61}}{\dfrac{60}{61}}\\\\\tan A=\dfrac{11}{60}$

Therefore,

$\tan A=\dfrac{11}{60}$