Question 198569
Recall that *[Tex \LARGE \sin^2(\theta)+\cos^2(\theta)=1]


So if *[Tex \LARGE \cos(\theta)=0.8], then *[Tex \LARGE \cos^2(\theta)=0.8^2=0.64]. Plug this into the identity above to get:



*[Tex \LARGE \sin^2(\theta)+0.64=1]



Now solve for *[Tex \LARGE \sin^2(\theta)]:


*[Tex \LARGE \sin^2(\theta)=1-0.64=0.36]



*[Tex \LARGE \sin(\theta)=\sqrt{0.36}=0.6]



Now because *[Tex \LARGE 270< \theta < 360], this means that the value of sine will be negative. 



So this means that *[Tex \LARGE \sin(\theta)=-0.6]



Now recall the identity: *[Tex \LARGE \sin(2\theta)=2\sin(\theta)\cos(\theta)]



*[Tex \LARGE \sin(2\theta)=2\sin(\theta)\cos(\theta)] ... Start with the given identity



*[Tex \LARGE \sin(2\theta)=2(-0.6)(0.8)] ... Plug in *[Tex \LARGE \sin(\theta)=-0.6] and *[Tex \LARGE \cos(\theta)=0.8]



*[Tex \LARGE \sin(2\theta)=-0.96] ... Multiply



So *[Tex \LARGE \sin(2\theta)=-0.96] which means that the answer is A) -0.96. So you are correct. Good job.