How Do You Find Tan(Theta) Given Sin(Theta/2)?

[lovemake1]

Homework Statement

find tan(theta) if sin (theta/2) = 3/5

Homework Equations

sin(theta/2) = sqrt[(1-cosx)/2]

The Attempt at a Solution

my attempt:

first since we know the half angle formula for sin, let sqrt[(1-cosx)/2] = 3/5
simplifying the equation, we get that cos(Theta) = 7/25 which is adjacent/hypothenus.
using this, we can calculate the value of opposite using pythagoras theorum. which is 24 in this case. since tan = sin/cos and sin = 24/25 and cos = 7/25
tan(Theta) = sin/cos which is 7/24

is this the most correct approach to take from what the question is asking?
please i would like to know if this will earn me full marks on a test or exam.

Thanks,

 

[JonF]

Homework Statement

find tan(theta) if sin (theta/2) = 3/5

Homework Equations

sin(theta/2) = sqrt[(1-cosx)/2]

The Attempt at a Solution

my attempt:

first since we know the half angle formula for sin, let sqrt[(1-cosx)/2] = 3/5
simplifying the equation, we get that cos(Theta) = 7/25 which is adjacent/hypothenus.
using this, we can calculate the value of opposite using pythagoras theorum. which is 24 in this case. since tan = sin/cos and sin = 24/25 and cos = 7/25
tan(Theta) = sin/cos which is 7/24

is this the most correct approach to take from what the question is asking?
please i would like to know if this will earn me full marks on a test or exam.

Thanks,

very close, redo this step: "since tan = sin/cos and sin = 24/25 and cos = 7/25"

Or just use tan = opp/adj