Question

Find the value of sin 660 degree + sin 780 degrees

Answer 1

Answer:

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Step-by-step explanation:

so basically sin 660 can be written as sin(720-60) degrees

so we know that sin 720=4π

so we know that whenever there is pi in any trigonometric ratio,there is no change

hence sin 660=sin 60

thus sin 60= √3/2

but according to Cartesian system sin 660 lies in fourth quadrant

and we know that except cos and sec all other trigonometric ratios are negative in fourth quadrant

thus sin 660= -√3/2

similarly sin 780=sin(720+60)

so again there would be no change

ie sin 780=sin 60

so as sin 780 lies in first quadrant,,sin 780 would be positive

thus we know that

sin 60=√3/2

hence sin 780=√3/2

thus then

sin 660 degree + sin 780 degrees

=-√3/2+√3/2

=0

hence value of sin 660 degrees+sin 780 degrees is 0