Download Tutorial Chapter 3 (Trigonometry)

LINEAR ALGEBRA
Tutorial Chapter 3
Question 1
Convert the following:
(a)
1 radian to degrees
(b)
3.1 radians to degrees
(c)
π/4 radians to degrees
(d)
60° to radians
(e)
357° to radians
Question 2
Find the length of the arc of a circle with radius 4 cm and central angle 5.1 radians.
Question 3
Find the area of the sector with radius 7 cm and central angle 2.5 radians.
Question 4
A bicycle with tyres 90 cm in diameter is travelling at 25 km/h. What is the angular
velocity of the tyre in radians per second?
Question 5
The propeller on a motorboat is rotating at 130 rad/s. What is the linear velocity of a point
on the tip of a blade if the blade is 22.5 cm long?
Question 6
Find the exact value of sin θ if the terminal side of θ passes through (7, 4).
Question 7
Find the exact values of all 6 trigonometric ratios of θ if the terminal side of θ passes
through (2, 10).
Question 8
Solve the triangle ABC, given that A = 35° and c = 15.67.
Question 9
The angle of elevation of an aeroplane is 23°. If the aeroplane’s altitude is 2500 m, how
far away is it?
Question 10
What is the sign (+ or -) of
(a)
sin(100°)
(b)
sec(-15°)
(c)
cos(188°)
Question 11
Find 2 angles whose cosine is 0.7.
Question 12
If tan θ = -0.809 and csc θ > 0, find cos θ.
Question 13
Prove that
tan y
 sec y
sin y
Question 14
Prove that
sin x cos x tan x = 1 − cos2 x
Question 15
Find the exact value of cos 75° by using 75° = 30° + 45°.
Question 16
If sin α = 4/5 (in Quadrant I) and cosβ = − 12/13 (in Quadrant II) evaluate sin(α − β).
Question 17
Find cos 60° by using the functions of 30°.
Question 18
Write the product cos 3t sin t as a sum or difference.
Question 19
Write the difference sin 7  sin 3 as a product.
Question 20
Find the exact value of sin 105  sin 15 using appropriate sum-to-product identity.
Question 21
Solve the equation sin 2θ = 0.8 for 0 ≤ θ < 2π.
Question 22
Solve the equation 6 sin2θ − sin θ − 1 = 0 for 0 ≤ θ < 2π.
Question 23
(a)
Express 4 sin θ + 3 cos θ in the form R sin(θ + α).
(b)
Using your answer from part (a), solve the equation
4 sin θ + 3 cos θ = 2
for 0° ≤ θ < 360°.
Question 24
The current I (in amperes) at time t in a particular circuit is given by
I = 12 sin t + 5 cos t.
Find the maximum current and the first time that it occurs.
Question 25
Find cos (sin -1 0.5)
Question 26
Sketch one cycle of the following without using a table.
(a)
y = sin t
(b)
v = cos t
(c)
E = -4 cos t
Question 27
Sketch 2 cycles of y = 3 cos 8x.
Question 28
Sketch
Question 29
Graph y = sin(2x + π/6)
Question 30
A point on a cam is 8.30 cm from the centre of rotation. Sketch 2 cycles of d as a function
of t, given that d = 0 cm when t = 0 s and ω = 3.20 rad/s.
Question 31
The voltage of an alternating current circuit is given by
e = E cos(ωt + α).
Sketch 2 cycles of the voltage as a function of time if
E = 80 V, ω = 377 rad/s and α = π/2.