Other Trigonometric Applications

Non Right Triangle Trig

100

This is one of the laws of cosine.

What is a²=b²+c²-2bccos(A)/b²=a²+c²-2accos(B)/c²=a²+b²-2abcos(C)?

200

This is the term for when the law of sines can produce two triangles.

What is the ambiguous case?

300

This is the measure of angle B if A=38^o, a=40, and b=52.(Round to one decimal place)

What is 53.2^o or 126.8^o?

400

These are the missing measurement in a triangle if A=110^o, c=30, and b=35(Round final answers to one decimal place).

What are a=53.3, B=38.1^o, and C=31.9^o?

500

A mailtruck leaves Bearingville at a bearing of N70^oW for 3 hours at 65mph. He stops in Circumcity to deliver a package, then leaves at a bearing of N25^oE for Areatown for 2 hours at 45mph. How far is Areatown from Bearingville?

207.5mi

Vectors

100

These are the two defining qualities of a vector.

What are magnitude and direction?

200

Given a horizontal component of 1 and a vertical component of 3, this is the magnitude of the resultant vector.

What is √10?

300

This is the resultant vector of performing (3i+4j)-(12i-5j)

What is -9i+9j?

400

Given A=<7,3> and B=<3,4>, this is the dot product of A and 2B.

What is 66?

500

A force of 100N and a force of 250N act on the same point 75^o apart. This is the magnitude of resultant force.

What is 292N?

Complex Numbers

100

This is the definition of i.

What is √-1?

200

This is 2+2√3i in trig form.

What is 4cis(60^o)?

300

This is the product of 2cis(30^o) and 4cis(60^o) in trig form.

What is 8cis(90^o)?

400

This is (3+3i√3)⁶ in standard form.(This question is worth double points!)

What is 46656?

500

These are all the sixth roots of 1 in polar form.

What are cis(0^o), cis(60^o), cis(120^o), cis(180^o), cis(240^o), and cis(300^o)?

Polar Equations And Graphs

100

This is the cartesian form of r=2.

What is x²+y²=4?

200

This is the polar form of y=2x-4(solved for r).

What is r=-4/(sinθ-2cosθ)?

300

This is the conic name of r=2sinθ.

What is a circle?

400

This is the polar intersection between r₁=2+4cosθ and r₂=4+2cosθ.

What is (6,0)?

500

This is the name of the shape of the graph of r²=-4/cos2θ(You probably don't know this but why not)

What is a hyperbola?

Parametric Equations

100

(x(t),y(t))

This is the point on the curve of (t²,t) at t=2

What is (4,2)?

200

(x(t),y(t))

Find the standard equation of the line (2t,t-4)

y=1/2x-4

300

(x(t),y(t))

This is the shape of (t²,2t-4)

What is a parabola?

400

(x(t),y(t))

As t increases, what direction does the graph of (cos(t),sin(t)) rotate in?(Another double value!)

What is counterclockwise?

500

(x(t),y(t))

The point (7,5) lies on the curve (t+4,t²-4). What is t at this point?

t=3