If `(3sin2theta)/(1-cos2theta)=1/2` and `0^(@)letheta180^(@)` , then `theta`=

Options

A. `0^(@)`
B. `0^(@)" or "180^(@)`
C. `80.5^(@)`
D. `0^(@)" or "80.5^(@)`

Answer

C

Explanation

With your calculator in degree mode, plot the graphs of y=1/2 y=(3sin(2x))/(1-cos(2x)) in the window [0,180] by [-2,2], Use CALC/intersect to find the one point of intersection in the specified interval, at `80.5^(@)`.
An altenative solution is to cross-multiply the original equation and use the double angle formulas for sine and cosine, to get
`6sin2theta=1-costheta`
`12sinthetacostheta=1-(1_2sin^2theta)=2sin^2theta`
`6sinthetacostheta-sin^2theta=0`
`sintheta(6costheta-sintheta)=0`
Therefore, `sintheta=0` or `theta=6`. It follows that `theta=0^(@),80.5^(@)`. The first two solution make the denominator of the original equation equal to zero, so `80.5^(@)` is the only solution. [7]