Notice;
cos2x = 1-2(sinx)² --- (1).
Substituting (1) in the given equation.
½(3-6(sinx)²+3)+4sinx+1 = 0
3-6(sinx)²+3+8sinx+2 = 0
6(sinx)²-8sinx-8 = 0
Calculating sinx.
Let sinx be p.
6p²-8p-8 =...
sinxcos60+sin60cosx-(cosxcos45+sinxsin45) = 0
0.5sinx+½(√(3)cosx)-½(√(2)cosx)-½(√(2)sinx) = 0
0.5sinx-½(√(2)sinx) = ½(√(2)cosx)-½(√(3)cosx)
sinx(1-√(2)) = cosx(√(2)-√(3))
sinx = ((√(2)-√...
Sir Mike Ambrose is the author of the question.
Let the side length of the regular pentagon be 2 unit.
Therefore the angle theta is;
asin(2sin42÷1.65418183057)
= 54°
Area green is;
Area...
Calculating yA.
Notice;
xA = 4
And y = (16+e^(0.5x))/4
y = ¼(16+e²)
Where y is yA.
Therefore;
Shaded Area as a single fraction is;
Area Rectangle with width 4 units and length ¼(16+e²) units - A...
Sir Mike Ambrose is the author of the question.
Let the two equal lengths be 1 unit.
(a) Calculating Theta exactly.
Let theta be x.
Calculating x.
x = ½(90-54)
x = ½(36)
x = 18°
sin18 = a/1
a = 0....
Let the single side length of the regular dodecagon be be 1 unit.
Therefore;
Area purple is;
Area triangle with height √(3) unit and base 1 unit.
= ½*√(3)*1
= ½√(3) square unit.
Area ABCD (squar...
Area Red Total in 1 d. p. Square unit is;
Area Square with side 2√(2) unit - Area triangle with height 2√(2) unit and base 1.1313708499 unit + Area triangle with two side √(13) unit and 3.285714285...
Let the regular pentagon side length be 1 unit.
a =⅕(180(5-2))
a = ⅕(180*3)
a = 108°
a is an angle of the regular pentagon.
Calculate x.
b = 108-90
b = 18°
x = ½(180-18)
x = ½(162)...
a = atan(⅓)°
⅓ = b/3
b = 1 unit.
It implies;
Area Red is;
Area triangle with height 1 unit and base 3 units + ½(2(area quarter circle with radius 3 units - area triangle with height and base 3 un...
Let DE be 1 unit.
AC = 4 units.
Area ABC is;
8sin60
= 4√(3) square units.
a² = 1+2²-4cos45
a = 1.47362575821 units.
(1.47362575821/sin45) = (1/sinb)
b = 28.6750500631°
c = 60-b
c = 31.3249499369...
