Home
::
About Us
::
Tutor in Your Home
::
Tutoring Center
::
SUMMER CAMP
::
Advertise With Us
::
College Counseling
::
Contact Us
Math is Fun
This site is an online mathematics and science school
where you can study without leaving your home (online education).
"
Do not worry about your difficulties in mathematics, I assure you that mine are greater
". Einstein, Albert (1879-1955)
Login
::
Sign Up - FREE
::
Refer a Friend
Study Guide
School of Logical Thinking
Tests Examples - Demo
Elementary Mathematics
High School Placement
Placement College Test
ACT
SAT
Flash Games
ACT
ACT Assessment
Test Description
English Test
Mathematics Test
Reading Test
Science Test
Writing Test
SAT
Early Mathematics
Study Guide
Arithmetic
Algebra
Geometry
Trigonometry
Trigonometric functions of any angle
To build all trigonometry, laws of which would be valid for any angles ( not only for acute angles, but also for obtuse, positive and negative angles), it is necessary to consider so called a unit circle, that is a circle with a radius, equal to 1 ( Fig.3 ).
Let draw two diameters: a horizontal AA’ and a vertical BB’. We count angles off a point A (starting point). Negative angles are counted in a clockwise, positive in an opposite direction. A movable radius OC forms angle with an immovable radius OA. It can be placed in the 1-st quarter ( COA ), in the 2-nd quarter ( DOA ), in the 3-rd quarter ( EOA ) or in the 4-th quarter ( FOA ). Considering OA and OB as positive directions and OA’ and OB’ as negative ones, we determine trigonometric functions of angles as follows.
A sine line of an angle ( Fig.4 ) is a vertical diameter of a unit circle, a cosine line of an angle - a horizontal diameter of a unit circle. A sine of an angle ( Fig.4 ) is the segment OB of a sine line, that is a projection of a movable radius OK to a sine line; a cosine of an angle - the segment OA of a cosine line, that is a projection of a movable radius OK to a cosine line.
Signs of sine and cosine in different quarters of a unit circle are shown on Fig.5 and Fig.6.
A tangent line ( Fig.7 ) is a tangent, drawn to a unit circle through the point A of a horizontal diameter.
A cotangent line ( Fig.8 ) is a tangent, drawn to a unit circle through the point B of a vertical diameter.
A tangent is a segment of a tangent line between the tangency point A and an intersection point ( D, E, etc., Fig.7 ) of a tangent line and a radius line.
A cotangent is a segment of a cotangent line between the tangency point B and an intersection point ( P, Q, etc., Fig.8 ) of a cotangent line and a radius line.
Signs of tangent and cotangent in different quarters of a unit circle see on Fig.9.
Secant and cosecant are determined as reciprocal values of cosine and sine correspondingly.
Return Back
View My Stats
Privacy Statement
© 2006 MathPlusFun, All Rights Reserved