# Pre-Calculus Chapter 6: Applications of Trigonometry

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Last updated 8 years ago

Discipline:
Math
Subject:
Pre-Calculus
10,11

Pre-Calculus Chapter 6: Applications of Trigonometry

Vocabulary Directed line segment (arrow)- The notation PQ denoting the directed line segment with initial point P and terminal point Q Position Vector of (a,b)- The vector {a,b}component form- {a,b} (or {a,b,c})standard representation- A representative arrow with its initial point at the origin magnitude of v- is the square root of a2 + b2direction- A vector in the direction of a line in three dimensional space zero vector- The vector {0,0} initial point- In ray PQ, P terminal point- In ray PQ, Qequivalent- Vectors with the same magnitude and directionscalars- A real number sum (resultant) of the vectors u and v- {u1, u2} + {v1, v2} = {u1 + v1, u2 + v2}product of the scalar k and the vector u- ku = {ku1, ku2}unit vector- Vector of length 1parallelogram- Geometric representation of vector addition using the parallelogram determined by the position vectorsunit vector in the direction of v- A unit vector that has the same direction as the given vector standard unit vectors- In the plane i= {1,0} and j= {0,1}linear combination- an expression au + bv, where a and b are real numbers direction angle- The angle the arrow makes with the positive x-axisresolving the vector- finding the horizontal and vertical components of a vector velocity- A vector that specifies the motion of an object in terms of its speed and direction speed- The magnitude of the velocity vector, given by distance/time dot product (inner product)- the number found when the corresponding components of two vectors are multiplied and then summed angle between u and v- The angle formed by two nonzero vectors sharing a common initial point orthogonal- two vectors u and v with the dot product of u and v= 0work- the product of a force applied to an object over a given distancecomplex plane- A coordinate plane used to represent the complex numbers.real axis- the x-axis of the complex planeimaginary axis- the y-axis of the complex plane trigonometric form (polar form)- r(cosѲ + isinѲ)argument- The argument of a + bi is the direction angle of the vector {a,b}nth root of z- a complex number v such that vn=znth root of unity- A complex number v such that vn=1

Helpful WebsitesDot Product of VCalculating Vector MagnitudeTail Minus Head RuleFinding Vector Components

Real World Applications

Vectors are used in theoretical physics in the area of quantum mechanics. A complete understanding of them are necessary in this career field. Mechanical engineers also use properties of trigonometry. They design and build various machines and tools. They would need to have to understand work and force.

De Moivre's Theorem

Angle Between Two Vectors