Question 980061
I'll do the first two parts to get you started.


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a)


300 degrees is in quadrant IV. The reference angle formula for quadrant IV is


R = 360 - x


where R is the reference angle and x is the given angle, so, 


R = 360 - x
R = 360 - 300
R = 60


Now use either a 30-60-90 triangle, or a unit circle to find that {{{sin(60) = (sqrt(3))/2}}}


Because this angle (300 degrees) is in Q4, we know sine is negative


{{{sin(300) = -sin(60) = -(sqrt(3))/2}}}


Final Answer: {{{sin(300) = -(sqrt(3))/2}}}

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b)


{{{tan(a+b) = (tan(a)+tan(b))/(1-tan(a)*tan(b))}}}


{{{tan(360+45) = (tan(360)+tan(45))/(1-tan(360)*tan(45))}}}


{{{tan(360+45) = (0+1)/(1-0*1)}}}


{{{tan(360+45) = (0+1)/(1-0)}}}


{{{tan(360+45) = 1/1}}}


{{{tan(360+45) = 1}}}


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So, {{{tan(360+45) = tan(405) = 1}}}