sin30=cos60=1/2. Quick way to remember sines and cosines of 30 and 60 is to draw an equilateral triangle of side length 2. All the angles are 60.Then draw a perpendicular line from the apex to the midpoint of the base.Now you have a 60 degree angle and a 30 degree angled triangle.By Pythagoras you will see that sin30=1/2,sin60=(sqrt3)/2 etc. also,if you want sines and cosines of 45,draw a right-angled triangle whose sides are 1,1 and sqrt2. Good to have these as diagrams in an exam for quick reference.
+128579 By a trig identity, we have that.......
sin Θ = cos (90 - Θ) so
sin 30° = cos (90 - 30)° = cos 60°
sin30=cos60=1/2. Quick way to remember sines and cosines of 30 and 60 is to draw an equilateral triangle of side length 2. All the angles are 60.Then draw a perpendicular line from the apex to the midpoint of the base.Now you have a 60 degree angle and a 30 degree angled triangle.By Pythagoras you will see that sin30=1/2,sin60=(sqrt3)/2 etc. also,if you want sines and cosines of 45,draw a right-angled triangle whose sides are 1,1 and sqrt2. Good to have these as diagrams in an exam for quick reference.
