5.4 Solve Trigonometric Equations
Chapter
Chapter 5
Section
5.4
Solutions 44 Videos

Determine approximate solutions for each equation in the interval x\in [0, 2\pi] to the nearest hundredth of a radian.

 \displaystyle \sin x -\frac{1}{4} = 0 

0.54mins
Q1a

Determine approximate solutions for each equation in the interval x\in [0, 2\pi] to the nearest hundredth of a radian.

 \displaystyle \cos x +\frac{3}{4} = 0 

1.40mins
Q1b

Determine approximate solutions for each equation in the interval x\in [0, 2\pi] to the nearest hundredth of a radian.

 \displaystyle \tan x - 5= 0 

0.50mins
Q1c

Determine approximate solutions for each equation in the interval x\in [0, 2\pi] to the nearest hundredth of a radian.

 \displaystyle \sec x - 4= 0 

1.01mins
Q1d

Determine approximate solutions for each equation in the interval x\in [0, 2\pi] to the nearest hundredth of a radian.

 \displaystyle 3\cot x + 2= 0 

1.33mins
Q1e

Determine approximate solutions for each equation in the interval x\in [0, 2\pi] to the nearest hundredth of a radian.

 \displaystyle 2\csc x + 5= 0 

1.37mins
Q1f

Determine exact solutions for each equation in the interval x\in [0, 2\pi].

 \displaystyle \sin x + \frac{\sqrt{3}}{2} = 0 

1.12mins
Q3a

Determine exact solutions for each equation in the interval x\in [0, 2\pi].

 \displaystyle \cos x - 0.5 = 0 

0.40mins
Q3b

Determine exact solutions for each equation in the interval x\in [0, 2\pi].

 \displaystyle \tan x - 1= 0 

0.36mins
Q3c

Determine exact solutions for each equation in the interval x\in [0, 2\pi].

 \displaystyle \cot x + 1= 0 

1.07mins
Q3d

Determine approximate solutions for each equation in the interval x\in [0, 2\pi], to the nearest hundredth of a radian.

\sin^2x -0.64 = 0

1.23mins
Q5a

Determine approximate solutions for each equation in the interval x\in [0, 2\pi], to the nearest hundredth of a radian.

\cos^2x -\frac{4}{9} = 0

1.27mins
Q5b

Determine approximate solutions for each equation in the interval x\in [0, 2\pi], to the nearest hundredth of a radian.

\tan^2x -1.44 = 0

1.34mins
Q5c

Determine approximate solutions for each equation in the interval x\in [0, 2\pi], to the nearest hundredth of a radian.

\sec^2x -2.5 = 0

1.59mins
Q5d

Determine approximate solutions for each equation in the interval x\in [0, 2\pi], to the nearest hundredth of a radian.

\cot^2x -1.21 = 0

1.47mins
Q5e

Determine exact solutions for each equation in the interval x\in [0, 2\pi].

 \displaystyle \sin^2x - \frac{1}{4} = 0 

1.02mins
Q7a

Determine exact solutions for each equation in the interval x\in [0, 2\pi].

 \displaystyle \cos^2x - \frac{3}{4} = 0 

1.30mins
Q7b

Determine exact solutions for each equation in the interval x\in [0, 2\pi].

 \displaystyle \tan^2x - 3 = 0 

1.26mins
Q7c

Determine exact solutions for each equation in the interval x\in [0, 2\pi].

 \displaystyle 3\csc^2x - 4 = 0 

1.42mins
Q7d

Solve \sin^2x - 2\sin x - 3 =0 on the interval x\in [0, 2\pi].

0.57mins
Q9

Solve \csc^2x - \csc x - 2 =0 on the interval x\in [0, 2\pi].

1.15mins
Q10

Solve 2\sec^2x + \sec x - 1 =0 on the interval x\in [0, 2\pi].

1.14mins
Q11

Solve \tan^2x + \tan x - 6 =0 on the interval x\in [0, 2\pi]. Round answers to the nearest hundredth o a radian.

2.24mins
Q12

Determine approximate solutions for each equation in the interval 2x \in [0, \pi], to the nearest hundredth of a radian.

\sin 2x - 0.8 = 0

1.07mins
Q13a

Determine approximate solutions for each equation in the interval 2x \in [0, \pi], to the nearest hundredth of a radian.

5\sin 2x - 3 = 0

1.05mins
Q13b

Determine approximate solutions for each equation in the interval 2x \in [0, \pi], to the nearest hundredth of a radian.

-4\sin 2x + 3 = 0

0.58mins
Q13c

Solve 2\tan^2x + 1 = 0 on the interval x\in [0, 2\pi].

0.41mins
Q14

Solve 3\sin 2x - 1 = 0 on the interval x\in [0, 2\pi].

1.49mins
Q15

Solve 6\cos^2x - 5\cos x - 6 = 0 on the interval x\in [0, 2\pi].

2.03mins
Q16

Solve 3\csc^2x - 5\csc x -2 = 0 on the interval x\in [0, 2\pi].

1.16mins
Q17

Solve \sec^2x + 5\sec x + 6 = 0 on the interval x\in [0, 2\pi].

2.34mins
Q18

Solve 2\tan^2x - 5\sec x -3 = 0 on the interval x\in [0, 2\pi].

2.18mins
Q19

Consider the trigonometric equation 3\sin^2x + \sin x - 1 = 0.

• Explain why the left side of the equation cannot be factored.
0.59mins
Q20a

Consider the trigonometric equation 3\sin^2x + \sin x - 1 = 0.

Use the quadratic formula to obtain the roots.

0.36mins
Q20b

Consider the trigonometric equation 3\sin^2x + \sin x - 1 = 0.

Determine all solutions in the interval x \in [0, 2\pi].

1.29mins
Q20c

The height, h, in metres, above the ground of a rider on a Ferris wheel can be modelled by the equation h = 10\sin(\frac{\pi}{12}(t - 7.5)) + 12, where t is the time, in seconds.

At t = 0 s, the rider is at the lowest point. Determine the first two times that the rider is 20 m above the ground, to the nearest hundredth of a second.

3.20mins
Q22

Consider the trigonometric equation 4\sin x \cos 2x + 4\cos x \sin 2x - 1 = 0 in there interval x \in [0, 2\pi]. Either show that there is no solution to the equation in this domain, or determine the smallest possible solution.

6.15mins
Q23

Consider the equation 2\cos^2x + \sin x - 1= 0.

Explain why the equation cannot be factored.

0.18mins
Q25a

Consider the equation 2\cos^2x + \sin x - 1= 0.

Suggest a trigonometric identity that can be used to factor.

0.50mins
Q25b

Consider the equation 2\cos^2x + \sin x - 1= 0.

i) Apply the identity and rearrange the equation into a factorable form.

ii) Factor the equation.

iii) Determine all solutions in the interval x \in [0, 2\pi].

1.01mins
Q25cdef

Determine solutions for \tan x \cos^2x -\tan x = 0 in the interval x \in [-2\pi, 2\pi].

2.03mins
Q26

The voltage, V, in volts, applied to an electric circuit can be modelled by the equation V = 167 \sin(120\pi t), where t is the time, in seconds. A component in the circuit can be safely withstand a voltage of more than 120 V for 0.01 s or less.

Determine the length of time that the voltage is greater than 120 V on each half-cycle.

2.45mins
Q27a

The voltage, V, in volts, applied to an electric circuit can be modelled by the equation V = 167 \sin(120\pi t), where t is the time, in seconds. A component in the circuit can be safely withstand a voltage of more than120 V for 0.01 s or less.

Is it safe to sue this component in this circuit? Just icy your answer.

0.25mins
Q27b

Determine solutions for

 \displaystyle \frac{\cos x}{1 +\sin x} + \frac{1 + \sin x}{\cos x} = 2 

in the interval x \in [-2\pi, 2\pi].

2.27mins
Q28
Lectures 13 Videos

Introduction to Solving Trig Equation with a linear equation with Trig example

3.01mins
Introduction to Solving Trig Equation with a linear equation with Trig example

Solving Trig Equation in ax^2+bx+c=0 form

2.01mins
Solving Trig Equation in ax^2+bx+c=0 form

Solving Trig Equation by Converting to Quadratic Equation form using Trig Identity

2.09mins
Solving Trig Equation by Converting to Quadratic Equation form using Trig Identity

Solving Trig Equation by simplifying it first using Double Angle Formula

2.48mins
Solving Trig Equation by simplifying it first using Double Angle Formula

Solving Trig Equation advanced example with sum of power of 6 of sin and cosine

3.28mins
Solving Trig Equation advanced example with sum of power of 6 of sin and cosine

Solving Trig Formula that requires simplification using Compounded Angle Formula

Solving Trig Equation in the form of A\sin x + B\cos x = C