MCR 3UTrig Applications & Functions Review

  1. Find the missing angle or side for these triangles.

a)b)The trunk of a leaning tree makes an angle of 12° with the vertical. To prevent the tree from falling over, a 35.0 m rope is attached to the top of the tree and is pegged into level ground some distance away. If the tree is 20.0 m from its base to its top, calculate the angle the rope makes with the ground to the nearest degree.

  1. What is the radian measure for these angles?

a)30˚b)- 45˚c)300˚

  1. a)Sketch the above angles in standard position.

b)What is the related acute angle for each of the above?

c)Write the principal angle for each.

d)What is the exact value for sine of each of the listed angles?

e)List one positive and one negative coterminal angle for each of the listed angles.

  1. In rational form, express the EXACT value of these trig ratios:

a)sin 30˚b)cos 45˚c)tan

  1. What is the CAST rule and what does it tell us?
  1. a) sin θ = b)cos θ = c)tan θ =

Given the ratios above

i)in which possible quadrants can the terminal arm be positioned?

ii)draw a diagram for each possible location found in part i).

iii)determine the two principal angles for 0° ≤ θ ≤ 360°.

  1. These next two questions correspond to the previous question above.

a)What is the related acute angle for each terminal arm in the previous question?

b)Provide 2 coterminal angles for each value of θ in the previous question.

  1. A point at P (-4, 2) is on the terminal arm of an angle θ in standard position. What is θ to the nearest tenth of a degree?
  1. Neatly sketch the graphs for the base functions ofy = sin θ and y = cos θ.
  1. For each equation below, state the amplitude, the period, the phase shift and the vertical shift.

a)b)c)

  1. Neatly graph each equation in the above question for –2π ≤ θ ≤ 2π.
  1. Determine the governing equation for each sine function shown below.

a)c)

b)d)

  1. Sketch the graph for a cosine function with an amplitude of 2, a phase shift of – π, and a period of π. What is the equation for the function?
  1. Meagan is sitting in a rocking chair. The distance, d (t), between the wall and the rear of the chair varies sinusoidally with time t. At t = 1s, the chair is closest to the wall and d (1) = 18 cm. At t = 1.75 s, the chair is farthest from the wall and d (1.75) = 34 cm.

a)What is the period of the function, and what does it represent in this situation?

b)How far is the chair from the wall when no one is rocking in it?

c)What is the equation of the sinusoidal function?

d)What is the distance between the wall and the chair at t = 8 s?

Extra Textbook practice:p. 484 #8, 9

p. 486 #8, 10, 11, 17, 20, 21, 25, 29

Answers:

1. a) b = 20.2; θ = 45˚; b) 34.0°; 2. a) ; b) ; c) ; 4. a) ; b) ; c) ; 6. a) III/IV; 210˚, 330˚; b) I/IV; 57.8˚, 302.2˚; c) I/III; 33.7˚, 213.7˚; 7. a) 30˚; 57.8˚; 33.7˚; b) 570°; 417.8°; -326.3°; 8. 153.4˚;

10. a) Amp = 2, Per = 2π, PS = -π, VS = 0; b) Amp = , Per = , PS = 0, VS = -1; c) Amp = 3, Per = π, PS =, VS = 0;

12. a) y = 2 sin ½θ; b) y = 3 sin 3 θ; c) y = 8 sin (2θ + ); d) y = 4 sin½(θ + π); 13. y = 2cos(2θ + );

14. a) 1.5 s; b) 26 cm; c) y = -8cos[240(t – 1)]+26; d) 30 cm

\mcr3U\trig\trig_functions_rvw_f09