We know that
2π/3 radians-------> convert to degrees-----> 2*180/3---> 120°
120°=90°+30°
Part a) Find <span>sin(2π/3)
</span>sin(2π/3)=sin (90°+30°)
we know that
sin (A+B)=sin A*cos B+cos A*sin B
so
sin (90°+30°)=sin 90*cos 30+cos 90*sin 30
sin 90=1
cos 30=√3/2
cos 90=0
sin 30=1/2
sin (90°+30°)=1*√3/2+0*1/2-----> √3/2
the answer part a) is
sin(2π/3)=√3/2
Part b) Find cos (2π/3)
cos (2π/3)=cos (90°+30°)
we know that
cos (A+B)=cos A*cos B-sin A*sin B
so
cos (90°+30°)=cos 90*cos 30-sin 90*sin 30
sin 90=1
cos 30=√3/2
cos 90=0
sin 30=1/2
cos (90°+30°)=0*√3/2-1*1/2----> -1/2
the answer part b) is
cos (2π/3)=-1/2
Answer:
x = -1
y = -9
Step-by-step explanation:
<u>A</u><u>d</u><u>d</u><u> </u><u>each linear equation:</u>
Sum: 5x = -5
<u>Divide each side by </u><u>5</u><u>:</u>
Quotient: x = -1.
<u>Substitute x = </u><u>-</u><u>1</u><u> into the </u><u>first</u><u> equation:</u>
4(-1) - y = 5
<u>Solve</u><u>:</u>
-4 - y = 5
<u>Add 4 to both sides of the equation:</u>
-y = 9
y = -9.
<u>Check with the second equation:</u>
-1 + -9 = -10.
Correct.
(x - y) • (y + 4)
Have a great day!
