Cumulative Review for Trig (pg 348)
Chapter
Chapter 5
Section
Cumulative Review for Trig (pg 348)
Solutions 19 Videos

Use the unit circle to determine exact values for the primary trigonometric ratios of 315°.

1.45mins
Q1

Use the unit circle to determine approximate values for the primary trigonometric ratios for 255°.

1.13mins
Q2

The coordinates of a point on the terminal arm of an angle \theta are (3, -1). Determine the exact trigonometric ratios of 6.

1.18mins
Q3

Angle Q is in the second quadrant, and \sin Q = \frac{15}{17} Determine values for \cos Q and \tan Q.

1.38mins
Q4

Solve the equation \tan \theta = - \frac{3}{8} for 0^o \leq \theta \leq 360^o.

1.33mins
Q5

Determine two angles between 0° and 360° that have a cosecant of -8.

1.28mins
Q6

Margit flies her small plane due west at 200 km/h for one hour. She turns right through an angle of 45°, and continues at the same speed for half an hour.

a) Sketch a diagram to illustrate this problem.

b) At the end of her flight, how far is Margit from her starting point?

1.28mins
Q7

Given \triangle ABC, such that a = 2.4 cm, c = 3.2 cm, and \angle A = 28°.

a) Draw two possible diagrams that match the given measurements.

b) Calculate the length of side b and the degree measure of the other two angles.

3.10mins
Q8

Detectors for subatomic particles known as neutrinos must be built far below ground to minimize interference from external sources of radiation. To reach such an underground laboratory, visitors start at an elevator building on the surface, descend straight down for 2.1 km, and walk east for 1.9 km to enter the lab. To reach the detector, the visitors turn left through an angle of 30°, and walk another 300 In. What is the straight-line distance, to the nearest tenth of a kilometre, from the elevator building to the detector?

2.39mins
Q9

In \triangle PQR, \angle P is 29°, p = 16 m, and q = 25 m. Determine all possible values for side r, to the nearest tenth of a metre.

2.33mins
Q10

Prove \displaystyle \sec \theta = \csc\theta \tan \theta 

0.26mins
Q11

Prove \displaystyle \csc \theta = \sin \theta + \cos^2\theta \csc \theta 

0.37mins
Q12

Consider the graph shown.

a) Explain why the function represented is periodic.

b) How many complete cycles are shown? c) What are the maximum and minimum values?

d) What is the amplitude?

e) What is the period?

1.54mins
Q13

Use a graph to determine the values of x for which \sin x = \cos x from -180° to 180.°

0.54mins
Q14

Consider the function \displaystyle y = 3\sin[2(x - 45^o)] - 1 

a) What is the amplitude?

b) What is the period?

c) Describe the phase shift.

d) Describe the vertical shift.

e) Graph the function for values of X from 0°t0 360°.

f) How would the equation change if the period were 90°?

3.20mins
Q15

A sinusoidal function has an amplitude of \displaystyle \frac{1}{2} units, a period of 1080°, and a maximum point at (0, \frac{3}{4}).

a) Represent the function with an equation using a sine function.

b) Draw a graph of the function over two cycles.

1.49mins
Q16

Consider the function \displaystyle f(x) = \frac{1}{4}\cos[2(x - 90^o)] 

a) Determine the amplitude, period, phase shift, and vertical shift with respect to y = \cos x.

b) What are the maximum and minimum values?

c) Find the first three X-intercepts to the right of the origin.

d) Find the y—intercept.

2.27mins
Q17

In some countries, water wheels are used to pump water to a higher level. An Egyptian water wheel pumps water from a level of -1.3 m up to 1.7 m. It completes a full turn in 15 s.

a) Use a sinusoidal function to model the height of the water as a function of time.

b) For your model, state the amplitude, period, phase shift, and vertical shift.

c) What is the height of the water at a time of 20 s?

1.52mins
Q18

The Snowbirds air demonstration team performs a vertical loop. The altitude and time data for the loop are shown in the table.

a) Use a sine function to model the altitude with respect to time.

b) Sketch a graph of your model for 4 cycles.

c) How does the function change if you use a cosine function?