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1 Answer
Feb 13, 2018

sine #330^@=-1/2#,
cosine #330^@=sqrt3/2#,
tangent #330^@=-1/sqrt3#

sine #((7pi)/4)=-1/sqrt2#,
cosine #((7pi)/4)=1/sqrt(2)#,
tangent #(7pi)/4=-1#

Explanation:

1)#330^@#
sine #330^@=sin330^@#
#=sin(360^@-30^@)#
#=sin(-30)^@#

The value of #sin(-30)^@=-1/2#
Hence,
sine #330^@=-1/2#

cosine #330^@=cos330^@#
#=cos(360^@-30^@)#
#=cos(-30)^@#

The value of #cos(-30)^@=sqrt3/2#
Hence,
cosine #330^@=sqrt3/2#

tangent #330^@=tan330^@#

#tan 330^@=sin330^@/cos330^@#

#=(-1/2)/(sqrt3/2)#
tangent #330^@=-1/sqrt3#

2) #(7pi)/4#
sine #(7pi)/4=sin(7pi)/4#
#=sin(2pi-(pi)/4)#
#=sin(-pi/4)#

The value of #sin(-pi/4)=-1/sqrt2#
Hence,
sine #((7pi)/4)=-1/sqrt2#

cosine #(7pi)/4=cos(7pi)/4#
#=cos(2pi-(pi)/4)#
#=cos((-pi)/4)#

The value of #=cos((-pi)/4)=1/sqrt2#
Hence,
cosine #((7pi)/4)=1/sqrt(2)#

tangent #(7pi)/4=tan(7pi)/4#

#tan (7pi)/4=(sin((pi)/4))/(cos((pi)/4))#

#=(-1/sqrt2)/(1/sqrt2)#
tangent #(7pi)/4=-1#