ALP 2

Vectors

100

Find the Magnitude and Direction. [0,2π)

<2,1>

magnitude: sqrt5

direction: 26.56 degrees

200

Determine the horizontal and vertical components of the vector with the given length and direction
lvl=20, Angle=30 degrees

Answer should be in i and j form

10sqrt3i+10j

300

u=<4,3> v=<9,1>

Find u+v, u-v, and 5u-2v

u+v=<13,-2>

u-v=<-5,-4>

5u-2v=<2,-17>

400

v=-3i+6j

Find a vector with initial point at the origin that is half the length and points in the same direction as v

<-3/2,3>

500

A woman leaves home and walks 2 miles west, then 7 miles southwest. How far from home is she? Round to the third decimal.

8.532 mi

Law of Sines

100

Solve the triangle.

Capitals=Angles, lower case=sides

B=34 degrees, C=82 degrees, a=5.6

A=64 degrees, c=6.2, b=3.5

200

Solve the triangle.

Capitals=Angles, lower case=sides

A=31 degrees, C=55 degrees, a=15

B=29.05 degrees, c=23.86, b=94

300

Bob is walking along a straight road. He decides to leave the road and walks on a path that makes an angle of 30 degrees with the road. After walking for 100 meters, he turns through an angle of 75 degrees and heads back toward the road. 

How far does Bob need to walk on his current path to get back to the road?

What is 100/sqrt2 meters

400

Solve the Triangle 

Capitals=Angles, lower case=sides

A = 60°, B = 60°, c = 60°

IMPOSSIBLE

500

Solve the Triangle

Capitals=Angles, lower case=sides

b = 3.7, c = 6.1, C = 70°

A=75.25°, B=34.75°, a=6.28

Law of Cosines

100

Determine the area of the triangle.

Capitals=Angles, lower case=sides

a=34, b=20, c=18

What is 144

200

Solve the triangle for the unknown side.

Capitals=Angles, lower case=sides

C= 49.1°, a = 2.51, b = 3.91

c=3

300

Capitals=Angles, lower case=sides

a = 47, b = 18, c = 33; find angle A.

A=132.1

400

Solve the triangle.

Capitals=Angles, lower case=sides

B = 83°, a = 4.6, c = 6.1

A=39.5° , C=57.5° , b=7.2

500

Find the area of a triangle with sides of length 12 in, 28 in, and 34 in. Round to the nearest tenth.

What is 158 in²

Solving Trig Functions and Equations

100

Determine the solution using identities.

2cos²(x)+3sin(x)-3=0

π /6, 5π /6,π /2

200

Determine the solutions using identities.

sec²(x)-2tan(x)=4

3π /4, tan^-1(3)

300

Determine the solution using identities. 

tan(x)+1=sec(x)

2π

400

Determine the solutions using identities.

sin(x)+cos(x)=1

2π ,π /2

500

Determine the solutions using identities.

4sin²(x)-3=0

π /3,2π /3,4π /3,5π /3

Polar

100

Convert this rectangular coordinate to a polar coordinate.

(-3,3)

(3sqrt2, 3π /4)

200

Convert this rectangular coordinate to a polar coordinate.

(-5,0)

(5,π)

300

Convert this rectangular coordinate to a polar coordinate.

(0,3)

(3,π/2)

400

Convert this rectangular equation to a polar equation.

x=4

r=4secθ

500

Convert this rectangular equation to a polar equation.

y=-x

θ =3π/4