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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
```

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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
```

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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
```

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0.50mins

Q1c

`x\in [0, 2\pi]`

to the nearest hundredth of a radian.

```
\displaystyle
\sec x - 4= 0
```

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1.01mins

Q1d

`x\in [0, 2\pi]`

to the nearest hundredth of a radian.

```
\displaystyle
3\cot x + 2= 0
```

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1.33mins

Q1e

`x\in [0, 2\pi]`

to the nearest hundredth of a radian.

```
\displaystyle
2\csc x + 5= 0
```

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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
```

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1.12mins

Q3a

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

.

```
\displaystyle
\cos x - 0.5 = 0
```

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0.40mins

Q3b

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

.

```
\displaystyle
\tan x - 1= 0
```

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0.36mins

Q3c

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

.

```
\displaystyle
\cot x + 1= 0
```

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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 `

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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 `

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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 `

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1.34mins

Q5c

`x\in [0, 2\pi]`

, to the nearest hundredth of a radian.

`\sec^2x -2.5 = 0 `

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1.59mins

Q5d

`x\in [0, 2\pi]`

, to the nearest hundredth of a radian.

`\cot^2x -1.21 = 0 `

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1.47mins

Q5e

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

.

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

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1.02mins

Q7a

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

.

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

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1.30mins

Q7b

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

.

```
\displaystyle
\tan^2x - 3 = 0
```

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1.26mins

Q7c

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

.

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

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1.42mins

Q7d

Solve `\sin^2x - 2\sin x - 3 =0`

on the interval `x\in [0, 2\pi]`

.

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0.57mins

Q9

Solve `\csc^2x - \csc x - 2 =0`

on the interval `x\in [0, 2\pi]`

.

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1.15mins

Q10

Solve `2\sec^2x + \sec x - 1 =0`

on the interval `x\in [0, 2\pi]`

.

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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.

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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`

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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`

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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`

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0.58mins

Q13c

Solve `2\tan^2x + 1 = 0`

on the interval `x\in [0, 2\pi]`

.

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0.41mins

Q14

Solve `3\sin 2x - 1 = 0`

on the interval `x\in [0, 2\pi]`

.

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1.49mins

Q15

Solve `6\cos^2x - 5\cos x - 6 = 0`

on the interval `x\in [0, 2\pi]`

.

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2.03mins

Q16

Solve `3\csc^2x - 5\csc x -2 = 0`

on the interval `x\in [0, 2\pi]`

.

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1.16mins

Q17

Solve `\sec^2x + 5\sec x + 6 = 0`

on the interval `x\in [0, 2\pi]`

.

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2.34mins

Q18

Solve `2\tan^2x - 5\sec x -3 = 0`

on the interval `x\in [0, 2\pi]`

.

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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.

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0.59mins

Q20a

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

.

Use the quadratic formula to obtain the roots.

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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]`

.

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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.

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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.

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6.15mins

Q23

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

.

Explain why the equation cannot be factored.

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0.18mins

Q25a

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

.

Suggest a trigonometric identity that can be used to factor.

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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]`

.

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1.01mins

Q25cdef

Determine solutions for `\tan x \cos^2x -\tan x = 0`

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

.

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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.

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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 than`120`

V for `0.01`

s or less.

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

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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]`

.

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2.27mins

Q28

Lectures
13 Videos

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

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3.01mins

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

Trig Equation in Quadratic Equation Form Differences of Squares

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2.28mins

Trig Equation in Quadratic Equation Form Differences of Squares

When the solution to Trig equation is not a special angle

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1.47mins

When the solution to Trig equation is not a special angle

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

form

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2.01mins

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

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

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2.09mins

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

Solving Trig equation with Double Angles

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4.11mins

Solving Trig equation with Double Angles

Solving Trig Equation with a Phase Shift

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2.44mins

Solving Trig Equation with a Phase Shift

Trig Equation with csc ratio and in Quadratic Form

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1.44mins

Trig Equation with csc ratio and in Quadratic Form

Solving Trig Equation by simplifying it first using Double Angle Formula

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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

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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

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2.42mins

Solving Trig Formula that requires simplification using Compounded Angle Formula

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

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2.48mins

Solving Trig Equation in the form of Asinx + Bsinx = C