Precal chapter 6 vocab

The third angle is found by subtracting the measure of the given angle and the angle found in the second step from ___

180°

True or false? Given two nonzero vectors v and w, v can be decomposed into two​ vectors, one parallel to w and the other orthogonal to w

True. It is always possible to decompose vector v into two​ vectors, because v1, the vector parallel to w, and v2, the vector orthogonal to w, can be found by decomposing the vector v

v=ai+bj, the horizontal component of v is __. The vertical component of v is __. The magnitude of v is given by ||v||= _________

a, b, √a²+b²

If​ A, B, and C are the measures of the angles of a​ triangle, and​ a, b, and c are the lengths of the sides opposite these​ angles, then the Law of Sines states that

a/sinA=b/sinB=c/sinC

The value √a²+b² is the ________ _____ of the complex number a+bi

absolute value

v=||v|| ____i+||v|| ____j

cosθ, sinθ

To test whether the graph of a polar equation may be symmetric with respect to the line θ=π/2 (y-axis), replace ____ with ____

(r,θ), (-r,-θ)

(r,θ)=(__, θ+π)

-r

To test if a polar equation may be symmetric with respect to the polar​ axis, replace θ by

-θ

The quotient of two complex numbers in polar form is found by _________ their moduli and __________ their arguments.

dividing, subtracting

If v=a1 i+ b1 j and w=a2 i+ b2 j are vectors, the product v*w, called the ____ ________, is defined as v*w=_________

dot product, a1*a2+ b1*b2

In the polar form of a complex​ number, r(cosθ+ i sinθ), r is called the ________ and θ is called the _______

modulus, argument

he product of two complex numbers in polar form is found by _______ their moduli and ________ their arguments.

multiplying, adding

The equation r=4 sinθ can be converted to a rectangular equation by _________ both sides by __ and then replacing r² with ______ and r sinθ with __

multiplying, r, x²+y², y

To solve an oblique triangle given three sides​ (SSS), the first step is to find the angle opposite the longest side using the Law of ______. Then we find either of the two remaining acute angles using the Law of______.

Cosines, sines

True or​ false: A triangle in which two sides and an angle opposite one of them are given​ (SSA) always results in at least one triangle.

False because an oblique triangle in which two sides and an angle are given results in an ambiguous case. The result may be one​ triangle, two​ triangles, or no triangle at all.

True or false? The definition of work indicates that work is a vector

False. The work W done by F in moving an object from A to B is defined W=F*AB. Since the result of the dot product is a​ scalar, work is a scalar.

The coordinate ​(5,135°) lies in quadrant

II

The coordinate (-7, -π/4) lies in quadrant

II

The coordinate (-8, π/4) lies in quadrant

III

The coordinate (-7, 135°) lies in quadrant

IV

The coordinate (3, -π/4) lies in quadrant

IV

The coordinate (4,5π/3) lies in quadrant

IV

Then we use the Law of ______ to find the angle opposite the shorter of the two given sides. This angle is always ______

Sines, acute

True or​ false? The graph of a polar equation may have symmetry even if it fails a test for that particular symmetry.

True

If​ A, B, and C are the measures of the angles of any triangle and if​ a, b, and c are the lengths of the sides opposite the corresponding​ angles, then which of the following is a form of the Law of​ Cosines?

b²= a²+c²-2ac cosB

In polar​ coordinates, the graphs of r=a cosθ and r=a sinθ are

circles

Every nonzero complex number has exactly __ distinct nth​ root(s).

n

A triangle that does not contain a right angle is called​ a/an ______ triangle. Solving such a triangle means finding the lengths of its _____ and the measurements of its ______

oblique, sides, angles

If v*w=0, then the two vectors v and w are _________

orthogonal

The foundation of the polar coordinate system consists of a​ point, called the_____, and a ray extending out from​ it, called the ________ _____

pole, polar axis

The origin in rectangular coordinates coincides with the _____ in polar​ coordinates; the positive​ x-axis in rectangular coordinates coincides with the _______ _____

pole, polar axis

(r,θ)=(__, θ+2π)

r

The equation x​+y=7 can be converted to a polar equation by replacing x with______ and replacing y with ______

r cosθ, r sinθ

To test whether the graph of a polar equation may be symmetric with respect to the​ pole(origin), replace ___ with ___

r, -r

r1(cosθ1+i sinθ1) /r2(cosθ2+i sinθ2)= _____[cos(_____)+i sin(_____)]

r1/r2, θ1-θ2, θ1-θ2

r1(cosθ1+i sinθ1) *r2(cosθ2+i sinθ2)= _____[cos(_____)+i sin(_____)]

r1r2, θ1+θ2, θ1+θ2

In the complex​ plane, the horizontal axis is referred to as the _____ axis and the vertical axis is called the _______ axis

real, imaginary

If F1 and F2 are two forces simultaneously acting on an object, the vector sum F1+F2 is called the ________ force

resultant

DeMoivre's Theorem states that [r(cosθ+i sinθ)]n= __[cos___+i sin___]

rn, (nθ), (nθ)

A quantity that has magnitude but no direction is called​ a/an _______

scalar

To solve an oblique triangle given two sides and an included angle​ (SAS), the first step is to find the missing_____ using the Law of _____

side, Cosines

We can always use the Law of Sines to find missing parts of triangles in which one _____ and two ______ are known

side, angles

The equation r=3 can be converted to a rectangular equation by_______ both sides and then replacing r² with _______

squaring, x²+y²

The equation θ=5π/4 can be converted to a rectangular equation by taking the ________ of both sides and then replacing tanθ with ____

tangent, y/x

The vectors i and j both have magnitudes of 1 and are called _____ vectors. The direction of vector i is along the positive __-axis. The direction of vector j is along the positive __-axis

unit, x, y

For any nonzero vector v, the unit vector that has the same direction as v is ______. To find this​ vector, divide v by its __________

v/||v||, magnitude

A ______ is a quantity that has both magnitude and direction

vector

If v and w are two nonzero vectors and θ is the smallest non negative angle between them, then v*w=_________

||v|| ||w|| cosθ

One method for graphing a polar equation is the​ point-plotting method. Substitute convenient values of __ into the equation and then determine the values for __

θ, r

​Heron's formula for the area of a triangle with sides​ a, b, and c is Area= _________ where s=

√(s(s-a)(s-b)(s-c) , 1/2(a+b+c)

To convert a complex number from rectangular​ form, z=a+bi, to polar form, z= r(cosθ+i sinθ), we use the relationships r=______ and tanθ=___ noting the quadrant in which the graph of z lies

√a²+b², b/a