Question

Given sinx=3/5 and x is in quadrant 2, what is the value of tan(x/2)

Answer 1

Answer:

3

Step-by-step explanation:

apex

Answer 2

X is in the second quadrant means that x/2 is in the first quadrant.


Consider the right triangle drawn in the figure. Let tan(x/2)=a.

Then, let the length of the opposite side to x/2 be a, the adjacent side be 1 and the hypotenuse be square root of a squared +1, as shown in the figure.

sin(x/2)=|opp side|/ |hypotenuse| =  $\frac{a}{ \sqrt{ a^{2}+1 } }$

cos (x/2) = |adj side|/ |hypotenuse| =  $\frac{1}{ \sqrt{ a^{2}+1 } }$


from the famous identity: sin(2a)=2sin(a)cos(a), we have:

2sin(x/2)cos (x/2)=sin(x)

thus

$2* \frac{a}{ \sqrt{ a^{2}+1 } }*\frac{1}{ \sqrt{ a^{2}+1 } }= \frac{3}{5}$

$2* \frac{a}{ a^{2}+1 }= \frac{3}{5}$

$10a=3 a^{2} +3$

$3 a^{2}-10a +3=0$

(3a-1)(a-3)=0

thus a=1/3 or a=3


thus tan(x/2)=1/3 or tan(x/2)=3


Answer: {1/3, 3}