Unit Circle
The Unit Circle is a circle with radius 1, centered in a coordinate system, where the x-axis is the cosine, and the y-axis is the sine. The Unit Circle is represented in the following figure, where we have added the $tan$ axis, tangent to the circle in point X (parallel to the $sine$ axis):
The Tangent Function
The tangent of an angle in a right triangle is given by the division between the length of the opposite side and the length of the adjacent side to the angle. In the right triangle OAC (previous figure) the tangent of angle $a$ is given by:
$tan(a)=\frac{(AC)}{(OC)}=\frac{sin(a)}{cos(a)}$
Triangles OAC and OTX have congruent internal angles. Thus
$tan(a)=\frac{(AC)}{(OC)}=\frac{(TX)}{(OX)}=\frac{(TX)}{1}=(TX)$, that is, the tangent of angle $a$ is point T in the $tan$ axis.
Between 0 and 90º the tangent function is positive and goes from zero to positive infinite when the angle approaches 90º. From 90 to 270º the tangent function goes from negative infinite to positive infinite (following graph).
The tangent has a period of 180º. That is,
$tan(x)=tan(x+180)=tan(x+2*180)=tan(x+n180)$, where $n$ is an integer, and $x$ is measured in degrees.
Consider, for example, $x=0º$. Thus,
$tan(0º)=tan(180º)=tan(360º)=tan(n180º)$
The Cotangent Function
The cotangent of an angle in a right triangle is given by the division between the length of the adjacent side and the length of the opposite side to the angle. That is,
$cotg(a)=\frac{cos(a)}{sen(a)}=\frac{1}{tan(a)}$
The Secant and the Cosecant Functions
The secant and the cosecant functions are defined as:
$sec(a)=\frac{1}{cos(a)}$
$cossec(a)=\frac{1}{sin(a)}$
Solved SAT Practice Tests
Find Practice Tests in the following link: (not available yet)
SAT Practice Tests - Tangent, Cotangent, Secant and Cosecant Functions and
Additional Practice Tests - Tangent, Cotangent, Secant and Cosecant Functions
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