ALP#1 Weeks 1-4

Triangles

100

A right triangle where both other angles besides the 90 degree one are equal.

What is a 45-45-90 triangle.

200

Find the length of the missing side using the Pythagorean theorem:

The hypotenuse measures 13

The opposite side measures 12

What is 5? 

Pythagorean theorem: a²+b² = c²

12² + b² = 13²

144+b² = 169

b² = 25

b= 5

300

Determine the area of a right triangle with its height measuring 5 and its base measuring 6.

What is 15?

Area of a triangle: (base*height)/2

(6*5)/2

30/2= 15

400

Suppose a plane is stuck in a storm and its position will stay the same for the next few minutes. Luckily, Superman can rescue the plane before the engine gives out. The plane is at a height of 12(in thousands of ft) and the diagonal distance Superman will travel to reach it is 15(in thousands of ft). At what angle will superman have to fly to reach the plane?

What is 53.1 degrees?

We know the height of the plane is 12 and the distance Superman will travel is 15. If we form a right triangle around this problem we find that we can find the angle by using the opposite/hypotenuse inverse sine function.  So sin^-1(12/15) = 53.1 degrees.

500

List all the trigonometric ratios.

What is sine, cosine, tangent, secant, cosecant, and cotangent?

The trigonometric ratios are those given by using the sides of a right triangle.

Angles and Radians

100

180 degrees is x radians.

pi/6 is y degrees. 

Find x and y.

What is pi for x and 30 degrees for y?

180* pi/180= pi

pi/6 *180/pi = 30

200

Find the coterminal angle of 390 degrees.

What is 30 degrees?

390 degrees-360(full circle) = 30

300

Given an arc with radius of 6m and angle of 4.45 radians, determine the arc length.

Arc length(s) = radius(r)*central angle(theta)

What is 26.7m?

4.45*6= 26.7m

400

Given an arc length of 20m, determine the radius if you know the angle is 7.89 radians.

What is 2.53m?

20/7.79 = 2.53

Trig Functions

100

Determine the quadrant in which the sin(x) is negative.

What is Quadrant 1 and 2?

200

Find x for which angles sine(x) = sqrt 2/2.

What is 3pi/4 and pi/4?

300

For the following function, identify the amplitude, period, phase shift and vertical shift:

f(x) = 3 sin(3pi/4 x +2) -9

The period is 3pi/4, the amplitude is 3, the phase shift is left 2 and vertical shift down 9.

400

Find the exact value of cos(17pi/12).

What is (sqrt 2- sqrt 6)/4?

Cos (8pi/12+9pi/12)= cos 2pi/3 cos 3pi/4- sin 2pi/3 sin 3pi/4.

sqrt 2/4 -sqrt 6/4.

We simplify and receive our answer

500

Simplify the following expression:

cot (x) * (cos (x)sin(x))/cos (x)

What is cos (x)?

cot (x) = cos(x)/sin(x)

cos(x)/sin(x) * (cos(x)sin(x))/cos(x)

Cosine gets cancelled on the bottom and sine gets cancelled on the top, so we are left with cos(x)