Question #8a799

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Answer 1 · 2018-02-15T16:02:48

#color(blue)(-56/65)#

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The unit circle can be expressed as:

#x^2+y^2=1#

We know #x=33/65#

#:.#

#(33/65)^2+y^2=1#

#y^2=1-(33/65)^2#

#(33/65)^2=33^2/65^2#

#y^2=1-33^2/65^2=(65^2-33^2)/65^2=3136/65^2#

#y=+-sqrt(3136/65^2)=56/65#

Since we are in the IV quadrant the #y# coordinate will be negative:

#-56/65#

#sin(theta)="opposite"/"hypotenuse"=(-56/65)/1=color(blue)(-56/65) #