Trigonometric Functions

Word Problems

100

The London Eye Ferris wheel has a diameter of 135m and completes one revolution in 30 minutes. Determine the angular velocity in radians per second.

W = pi/900 

200

The tides at Cape Capstan, New Brunswick, change the depth of the water in the rbour. On one day in October, the tides have a high point of approximately 10 m at 2 p.m. and a low point of approximately 1.2 m at 8:15 p.m. A particular sailboat has a draft of 2 m. This means it can only move in water that is at least 2 m deep. The captain of the sailboat plans to leave the harbour at 6:30 p.m. Can the captain exit the harbour safely at that time? What is the question you will be using.

Yes he can 

y=4.4cos4pi/25(x-2) +5.6

300

In a simple arc for an alternating current circuit, the current at any instant t is given by the iction f(t)=15sin(60t). Find the average rate of change as t goes from 2 to 3. Find the instantaneous rate of change at t = 2 

Aroc = -20.7

Iroc= 716.7

400

A small windmill has its center 6 m above the ground and blades 2 m in length.In a steady wind, a point P at the tip of one blade makes a complete rotation in 12 s.

a) Determine a function that gives the height of point P above the ground at a time t.

h(t)=-3cos(pi/20t) +2.5

500

During a bicycle race, the back wheel of Dillans bicycle rotates 120 times in 1 min. Determine the exact angular velocity of the wheel in degrees per second. 

720

Radian Measure

100

Change the following radian to degrees 

PI 

180 degrees 

200

Change the following from radians to degrees 

270

3pi/2

300

How are you to find the feda in a unit circle? 

feda = arc length divided by radius 

400

Determine the exact value of the trig ratio below 

sec11pi/6

cos11pi/6 = root3/2

500

Determine the exact value of the trip ratio below 

sin3pi/4

 

=1/root 2 

Transformations

100

what does "a" mean in transformation? 

Amplitude

200

The value of "d" is it a phase shift or a Vertical shift? 

Phase Shift 

300

When finding your values of "a" and "c" which of the following is an addition equation between your max and min values followed by being divided by 2. 

This would be your C value

400

In the equation below describes transformations that are occurring 

y= 1.5sin2(x-pi) +3

a - 1.5

period - pi

Scale - pi/4 

Vertical shift 3 units up 

500

A cosine function has a Max value of 8 and a minimum of -4, a period of 4pi, and a phase shift of pi. 

Create an equation for the function 

y= 6cos1/2(x+pi) +2 

Solving trig Equations

100

Determine the exact solution for 0<x<2pi

Cos +1 = 0 

x=Pi

200

Determine the exact solution for 0<x<2pi

Sin x = Root 3/2

x = pi/3, 2pi/3

300

Determine the approximate solution rounded to the nearest hundred 

sin x = 1/4 

x = 0.25, 2.89

400

Solve the following 

y=cos^2x+3 cos x+2=0

x=Pi

500

Solve the following 

2 cosxsinx = cosx

x = pi/2, 3pi/2

x = pi/6, 5pi/6

Definitions

100

In the CAST which quadrants are each of the following positive?

Tan, Cos, Sin

Sin - 1,2

Cos - 1,4

Tan - 3,4

200

Special Triangle what are the sidelengths when the angle is 45 degrees? 

Hyp - Root 2 

Opp - 1

Adj - 1

300

What does the Mid Line of curve mean 

The Mid-Line Curve is about the "c" value telling us whether the function is shifted left or right. 

400

What are your zero value? 

Your 0 is the same as your x intercepts

500

Name a similarity and difference between sine and cosine functions?

Difference- The sine function starts at origin while cosine starts at 1

Similarity- They both stay within the same max and min values and both have the same ways patters.