Trigonometry Flashcards
(17 cards)
What is the Opposite side (O)?
The side opposite the specified angle.
What is the Adjacent side (A)?
The side next to the specified angle.
What is sin(𝜃)?
O/H
What is cos(𝜃)?
A/H
What is tan(𝜃)?
O/A
What is sin(0°), sin(30°), sin(60°), sin(45°), sin(90°)?
0, 1/2, [rt2(3)]/2, [rt2(2)]/2, 1
What is cos(0°), cos(30°), cos(60°), cos(45°), cos(90°)?
1, [rt2(3)]/2, 1/2, [rt2(2)]/2, 0
What is tan(0°), tan(30°), tan(60°), tan(45°), tan(90°)?
0, [rt2(3)]/3, rt2(3), 1, Undefined
What is O?
Hsin(𝜃) or Atan(𝜃)
What is A?
Hcos(𝜃) or O/tan(𝜃)
What is H?
O/sin(𝜃) or A/cos(𝜃)
What are (sin^-1)(O/H), (cos^-1)(A/H) and (tan^-1)(O/A)?
Functions to the -1 are the inverse of the original function so all of these statements equal 𝜃.
What is the unit circle?
A circle with a radius of one that is put around the origin. The angle can then move around the circle and at any given angle, the x coordinate is cos(𝜃) and the y coordinate is sin(𝜃).
What forms do the graphs sin(x), cos(x) and tan(x) take?
sin(x) and cos(x) take the form of a wave with a maximum of 1 and a minimum of -1. The former hits the origin while the latter hits (0, 1). tan(x) takes the form of separate curved lines stretching to infinity.
If A is the angle opposite side a and B is the angle opposite side b etc. what is the sine rule?
a/sin(A) = b/sin(B) = c/sin(C) for any triangle. You can use it to work out a side when two angles and an opposite side are known and an angle when two sides and an opposite angle are known.
If A is the angle opposite side a, what is the cosine rule?
a^2 = b^2 + c^2 - 2bc cos(A) or cos(A) = (b^2 + c^2 - a^2)/2bc for any triangle. You can use it to work out a side when two sides and the angle in between them are known and an angle when three sides are known.
What can be used to find the area of a triangle?
If /c is the angle between a and b then the area is [ab sin(C)]/2.
