Direction Angles, Cosines, and Ratios

Loading the math board and drawing, please wait…

2018-02-03 09:45

This example illustrates the concepts of direction angles, cosines, and ratios. It involves basic knowledge of trigonometry and vectors. Using commands like rotation, intersection, and vector, users can dynamically explore the direction angles and cosine values of vectors in three-dimensional space. Suitable for high school mathematics education, particularly in coordinate geometry and vector courses.

GeoGebra Commands & Parameters

Intersect(xAxis, yAxis) → O
Circle(O, 1) → c_1
Intersect(c_1, xAxis, 2) → Q_1
Rotate(Q_1, θ_., O) → Q
Intersect(yAxis, xAxis) → A
Segment(A, P) → f
OrthogonalLine(P, xOyPlane) → g
Intersect(g, xOyPlane) → C
OrthogonalLine(C, xAxis, space) → h
Intersect(h, xAxis) → D
Segment(A, D) → i
Segment(D, C) → j
Vector(A, P) → u
Angle(D, A, P) → α
Point(yAxis) → B
Point(zAxis) → E
Angle(P, A, E) → γ
Angle(P, A, B) → β
Length(i) → x_.
Length(j) → y_.
OrthogonalLine(P, xAxis, space) → l
OrthogonalLine(P, zAxis, space) → m
OrthogonalLine(P, yAxis, space) → n
Intersect(l, xAxis) → F
Intersect(m, zAxis) → G
Intersect(n, yAxis) → H
Segment(F, A) → p
Segment(A, G) → q
Intersect(γ, yAxis, 1) → I
Intersect(yAxis, xAxis) → J
Segment(H, A) → s
Segment(P, F) → t
Segment(G, P) → c
Segment(H, P) → d
Length(p) → a_.
Length(s) → b_.
Length(q) → c_.
Midpoint(A, F) → K
Midpoint(A, H) → L
Midpoint(A, G) → M
Midpoint(f) → N
Angle(Q_1, O, Q) → θ_…
Segment(O, Q) → f_1
OrthogonalLine(Q, xAxis) → g_1
Intersect(g_1, xAxis) → R
Segment(Q, R) → h_1
Segment(R, O) → i_1
Midpoint(i_1) → S
Midpoint(h_1) → T
Vector(R, Q) → w
Vector(O, R) → u_1
Segment(P, C) → j_1
Segment(A, C) → k_1
Angle(A, C, P) → δ
Angle(A, D, C) → ε