Chapter 8 Triangle Trigonometry Flashcards
What is a trigonometric function?
Provide examples of one
They are functions defined in terms of triangles
Sine and Cosine are examples of this
In a right triangle, what is sine equal to, in order to get the angle for the triangle from the origin of the unit circle?
sin (D) =
Opposite Side / Adjacent To the origin angle side
In a right triangle, what is cosine equal to, in order to get the angle for the triangle from the origin of the unit circle?
Cos(D) =
Adjacent to the origin angle side / Hypotenuse
How would you solve for angles?
Using either inverse sine or inverse cosine or inverse tangent
sin^-1 or cos^-1 or tan^-1
In a right triangle, what is tan equal to, in order to get the angle for the triangle from the origin of the unit circle?
tan(D) =
Opposite Side / Adjacent to the origin angle side
What is the Law of Cosines?
For a triangle with sides a,b,c and angle C opposite of c, we have:
c^2 = a^2 + b^2 -2abCos(C)
What is the Law of Sines?
For a triangle with sides a,b,c opposite angles A,B,C respectively:
sin(A) sin(B) sin(C)
——— = ——— = ———
a b c
What is the ambiguous case?
It is the fact that the Law of Sines does not tell us the angle, but only it’s sine, and there are two angles between 0 and 180 degrees for each given sine
What is the polar opposite?
Coordinates derived from the distance(hypotenuse) from the origin and the angle such that (distance, angle)
What is the relationship between the x coordinate and polar coordinate?
X =r(cos(degrees))
What is the relationship between the y coordinate and polar coordinate?
Y= r(sin(degrees))
What is the formula for distance for the polar coordinate?
r=sqrt(x^2+y^2)
How is the formula for the angle using cosine?
Cos(degrees) = x/(sqrt(x^2+y^2)
What is the formula for the angle using sine?
Sin(degrees) = y /(sqrt(x^2+y^2)
Is it possible to derive the angle from the inverse tangent function?
No
