TRIGONOMETRY Flashcards
FATHER OF TRIGO
Hipparchus
TRIANGLE WITH 2 EQUAL SIDES
ISOSCLES TRIANGLE
TRIANGLE WHERE ALL SIDES ARE EQUAL
EQUILATERAL TRIANGLE
TRIANGLE WITH NO EQUAL SIDES
SCALENE TRIANGLE
ALL THREE INTERNAL ANGLE IS LESS THAN 90 DEGREE
ACUTE TRIANGLE
ONE INTERNAL ANGLE IS 90 DEGREE
RIGHT TRIANGLE
ONE INTERNAL ANGLE IS GREATER THAN 90 DEGREE
OBTUSE TRIANGLE
Tan^2(θ) + 1 =? & Cot^2(θ) +1 =?
=Sec^2 (θ) & =Csc^2(θ)
Sin(A±B)= ? & Cos(A±B0 = ?
=Sin(A)Cos(B)±Cos(A)Sin(B)
=Cos(A)Cos(B)∓Sin(A)Sin(B)
Tan(A±B)=?
=(TanA±TanB)/1∓TanATanB
Sin2θ=? & Cos2θ=?
=2SinθCosθ
=Cos^2(θ)-Sin^2(θ)
Tan^2θ=?
2Tanθ/(1-Tan^2(θ))
WHATI IS THE FORMULA OF SINE LAW AND WHEN IS IT USED.
- 2 SIDES AND ONE OPPOSITE ANGLE
OR - 2 ANGLE AND ONE OPPOSITE SIDE
formula:
a/SinA= b/SinB = c/SinC
WHAT IS THE FORMULA FOR COS LAW AND WHEN IS IT USED
*TWO SIDES AND AN INCLUDED ANGLE
OR
*THREE SIDES
FORMULA:
a^2= b^2 + c^2 - 2bcCosA
b^2= a^2 + c^2 - 2acCosB
c^2= a^2 + b^2 - 2abCosC
formula for AREA OF TRIANGLE! given 2 sides and an angle
A=1/2abSinθ
formula for area of triable! given 3 sides only.
use semi-perimeter formula where s=(a+b+c)/2
then A = √[s(s-a)(s-b)(s-c)]
A.K.A HERON’S FORMULA
INSCRIBE MEANS?
“INSIDE”
A TRIANGLE INSCRIBED IN A CIRCLE MEANS THAT THE TRIANGLE IS DRAWN “inside” the circle.
what is the formula of the radius of a circle that has a triangle inscribed in it.
r= (abc)/(4A) A= is the area of the triangle. r= radius of circle
what is the formula of the radius of a circle that has am equilateral triangle inscribed in it.
r=(a√3)/3
a= 1 side of the triangle.
what is the formula of the radius of a circle that has a right triangle inscribed in it.
r= hypotenuse /2
CIRCUMSCRIBE MEANS?
“OUTSIDE” SHAPE
WHAT IS THE FORMULA FOR THE RADIUS OF A CIRCLE THAT IS INSCIRBED IN A TRIANGLE, OR CIRCUMSCRIBED BY A TRIANGLE.
r=2A/a+b+c
A= area of triangle
WHAT IS THE FORMULA FOR THE RADIUS OF A CIRCLE THAT IS INSCIRBED IN AN EQUILATERAL TRIANGLE.
r=(L√3)/6
L= length of one side
WHAT IS THE FORMULA FOR THE RADIUS OF A CIRCLE THAT IS INSCIRBED IN A right triangle
r= (ab)/(a+b+c)
escribed means????
A CIRCLE DRAWN OUTSIDE A TRIANGLE THAT IS TANGENT TO ONE SIDE OF THE TRIANGLE
“LIKE A CIRCLE LEANING IN A TRIANGLE”
AREEA OF THE TRIANGLE ESCRIBE IN/WITH/BESIDE A CIRCLE
Area of triangle= A = r(s-a)
s= half the perimeter of a triangle.
a= side the circle is leaning against.
6 recirprovcal identites sin cos tan cot sec csc
sinθ=1/csc cosθ=1/sec tanθ=1/cot cotθ=1/tan secθ=1/cos cscθ= 1/sin
3 phytagorean identity (triigonometric identity)
sin^2θ + cos^2θ =1
1 + tan^2 θ = sec^2 θ
1 + cot^2 θ = csc^2 θ
