Intro to Trigonometry:
There are 6 trigonometric functions, which take angles as their input and output to a real number. An angle is said to be in standard position: x-axis, with it vertex at the origin. If the angle opens clockwise then the angle is considered to be negative angle. If the angle opens counter-clockwise it is considered to be a positive angle.
Two angles are called coterminal if they share a terminal side in standard position. For example, the angles 150 degrees, 510 degrees, and -210 degrees are all coterminal.
Radians are another unit of measure for angles. There are 360 degrees in a complete angle
so 360 degrees is equal to 2 pi radians; 180 degrees is equal to pi radians; 180 degrees divided by pi is equal to 1 or equal to pi divided by 180 degrees.
The unit circle is the circle centered at the origin with a radius the length of one unit.
The definition of the trig functions in the context of a point on the plane is suppose is in standard position, and p= (x,y) is a point on the terminal side of theta, and r is the distance between P and the origin. Then the six trig functions are defined as follows:
In the context if a point is on the unit circle. Suppose is in standard position , and P= (x,y) is a point on the unit circle. Then the 6 trig functions are defined as follows:
sin = y
cos = x
Definition of the trig functions in the context of a right triangle. Suppose is an acute angle of a right triangle. Trig functions are defined as follows:
x + x = 1
sin(x + y) = sin x cos y + cos x sin y
sin (x – y) = sin x cos y – cos x sin y
cos (x + y) = cos x cos y – sin x sin y
cos (x – y) = cos x cos y + sin x sin y
The derivative of y = sin x also depends on the value of
To esitmate the limit, find the qoutient for various calues of x close to 0. ( make sure to set your calculator to radian mode not in degree mode)
Derivatives of Trig Functions:
Dx(sin x) = cos x
Dx(cos x) = -sin x
Dx (tan x) = x
Dx (cot x) = x
Dx (sec x) = sec x tan x
Dx (csc x) = -csc x cot x