Question

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

Answer 1

3

Explanation:

i did the quiz

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 } }= (3)/(5)`


`2* (a)/( a^(2)+1 )= (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}