hello all what is trignometry and circle
Answers
Answer:
Trigonometry is a branch of Mathematics that involves the studies of triangles, relationships between their sides and the angles between the sides.
A circle is a shape that is created with all points on it at an equal distance from a fixed point which is called the center of the circle. The path created by the points is called the circumference of the circle. It has a diameter which is a line drawn from any one point on the circumference to another point on the circumference, but it runs through its center. Half of the diameter is the radius. The radius is a straight line drawn from the center to any point on the circumference.
Step-by-step explanation:
Step-by-step explanation:
TRIGONOMETRY:
DEFINITION:
Trigonometry is one of the important branches in the history of mathematics and this concept is given by a Greek mathematician Hipparchus. Here, we will study the relationship between the sides and angles of a right-angled triangle. The basics of trigonometry define three primary functions which are sine, cosine and tangent.
Trigonometry is one of those divisions in mathematics that helps in finding the angles and missing sides of a triangle with the help of trigonometric ratios. The angles are either measured in radians or degrees. The commonly used trigonometry angles are 0°, 30°, 45°, 60° and 90°.
MORE INFORMATION:
Trigonometry Angles
The trigonometry angles which are commonly used in trigonometry problems are 0°, 30°, 45°, 60° and 90°. The trigonometric ratios such as sine, cosine and tangent of these angles are easy to memorize. We will also show the table where all the ratios and their respective angle’s values are mentioned. To find these angles we have to draw a right-angled triangle, in which one of the acute angles will be the corresponding trigonometry angle. These angles will be defined with respect to the ratio associated with it.
For example, in a right-angled triangle,
Sin θ = Perpendicular/Hypotenuse
or θ = sin-1 (P/H)
Similarly,
θ = cos-1 (Base/Hypotenuse)
θ = tan-1 (Perpendicular/Base)
List of Trigonometry Formulas
The Trigonometric formulas or Identities are the equations which are true in the case of Right-Angled Triangles. Some of the special trigonometric identities are given below –
Pythagorean Identities
sin²θ + cos²θ = 1
tan2θ + 1 = sec2θ
cot2θ + 1 = cosec2θ
sin 2θ = 2 sin θ cos θ
cos 2θ = cos²θ – sin²θ
tan 2θ = 2 tan θ / (1 – tan²θ)
cot 2θ = (cot²θ – 1) / 2 cot θ
Sum and Difference identities-
For angles u and v, we have the following relationships:
sin(u + v) = sin(u)cos(v) + cos(u)sin(v)
cos(u + v) = cos(u)cos(v) – sin(u)sin(v)
tan(u+v) = tan(u) + tan(v) / 1−tan(u) tan(v)
sin(u – v) = sin(u)cos(v) – cos(u)sin(v)
cos(u – v) = cos(u)cos(v) + sin(u)sin(v)
tan(u-v) = tan(u) − tan(v) / 1+tan(u) tan(v)
If A, B and C are angles and a, b and c are the sides of a triangle, then,
Sine Laws
a/sinA = b/sinB = c/sinC
Cosine Laws
c2 = a2 + b2 – 2ab cos C
a2 = b2 + c2 – 2bc cos A
b2 = a2 + c2 – 2ac cos B
Trigonometry Identities
The three important trigonometric identities are:
sin²θ + cos²θ = 1
tan²θ + 1 = sec²θ
cot²θ + 1 = cosec²θ
CIRCLES:
DEFINITION:.
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry. Also, it has rotational symmetry around the centre for every angle. The circle formula in the plane is given as:
MORE INFORMATION:
(x-h)2 + (y-k)2 = r2
where (x,y) are the coordinate points
(h,k) is the coordinate of the centre of a circle
and r is the radius of a circle.
Parts of Circle
A circle has different parts based on the positions and their properties. The different parts of a circle are explained below in detail.
Annulus-The region bounded by two concentric circles. It is basically a ring-shaped object. See the figure below.
Arc – It is basically the connected curve of a circle.
Sector – A region bounded by two radii and an arc.
Segment- A region bounded by a chord and an arc lying between the chord’s endpoints. It is to be noted that segments do not contain the centre.
Centre – It is the midpoint of a circle.
Chord- A line segment whose endpoints lie on the circle.
Diameter- A line segment having both the endpoints on the circle and is the largest chord of the circle.
Radius- A line segment connecting the centre of a circle to any point on the circle itself.
Secant- A straight line cutting the circle at two points. It is also called an extended chord.
Tangent- A coplanar straight line touching the circle at a single point.