How do you remember the formula for the triogomentric functions?
The trigonometric functions sinex , cosinex and tangentx and the respective reciprocals cosecant x , secant x and cotangent x, where x is the angle other than the right angle.
To remember easily these functios are expressed interms of the sides right angled triangle.
Let ABC be right angled triangle with right angle at B. Letanle A = x.
Then sine A = Sine x = BC/AC = Opposite side/Hypotenuse.
cosineA = cosx = AB/AC = Adjacent side /Hypotenuse
tanA = tanx = sinx/cosx = BC/AB= Opposite side/ Adjacent side.
cosecantA = cosecantx = 1/sinex =AC/AB
secantA = 1/cosinex = AC/AB
cotangentx = 1/tangentx = AB/BC.
Thus the trigonometric functions could be easily remembered and calculated through the sides of the right angled triangle at least roughly.
We'll consider the right angled triangle, whose hypothenuse is the radius of the trigonometric circle.
The radius of trigonometric circle is R = 1 unit and the x and y axis have the origin in the center of trigonometric circle.
We'll express the trigonometric functions, sine and cosine:
sin a = opposite cathetus/hypothenuse
sin a = y/R
sin a = y/1
sin a = y
cos a = x/R
cos a = x
We notice that the functions sine and cosine could be expressed with respect to the x and y axis.
A Cat Sat
On An Orange
And Howled Horribly
you use the above statment and you place it in this way so it becomes for cos which is cat = adjacent which is an divided by Hypotenuse which is howled