Textbook

Advanced Functions Nelson
Chapter

Chapter 7
Section

Chapter Review of Trig Identities and Equations

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Solutions
33 Videos

Which trigonometric ratio is equivalent to the trigonometric ratio below.

```
\displaystyle
\sin \frac{3\pi}{10}
```

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0.48mins

Q1a

Which trigonometric ratio is equivalent to the trigonometric ratio below.

```
\displaystyle
\cos \frac{6\pi}{7}
```

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0.46mins

Q1b

Which trigonometric ratio is equivalent to the trigonometric ratio below.

```
\displaystyle
-\sin \frac{13\pi}{7}
```

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0.36mins

Q1c

Which trigonometric ratio is equivalent to the trigonometric ratio below.

```
\displaystyle
-\cos \frac{8\pi}{7}
```

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0.33mins

Q1d

Write an equation that is equivalent to

```
\displaystyle
y = -5\sin(x -\frac{\pi}{2}) - 8
```

, using the cosine function.

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0.51mins

Q2

Use a compound angle formula to determine a trigonometric expression that is equivalent to the expressions.

```
\displaystyle
\sin(x - \frac{4\pi}{3})
```

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1.09mins

Q3a

Use a compound angle formula to determine a trigonometric expression that is equivalent to the expressions.

```
\displaystyle
\cos(x + \frac{3\pi}{4})
```

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1.01mins

Q3b

Use a compound angle formula to determine a trigonometric expression that is equivalent to the expressions.

```
\displaystyle
\tan (x + \frac{\pi}{3})
```

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0.24mins

Q3c

```
\displaystyle
\cos(x - \frac{5\pi}{4})
```

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Q3d

Evaluate the expression.

```
\displaystyle
\frac{\tan \frac{\pi}{12} + \tan\frac{7\pi}{4}}{1 -\tan\frac{\pi}{12}\tan\frac{7\pi}{4}}
```

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1.07mins

Q4a

Evaluate the expression.

```
\displaystyle
\cos \frac{\pi}{9} \cos\frac{19\pi}{18} - \sin \frac{\pi}{9}\sin \frac{19\pi}{18}
```

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0.54mins

Q4b

Simplify the expression.

```
\displaystyle
2\sin \frac{\pi}{12}\cos\frac{\pi}{12}
```

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0.18mins

Q5a

Simplify the expression.

```
\displaystyle
\cos^2 \frac{\pi}{12} - \sin^2 \frac{\pi}{12}
```

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0.19mins

Q5b

Simplify the expression.

```
\displaystyle
1 - 2\sin^2\frac{3\pi}{8}
```

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0.39mins

Q5c

Simplify the expression.

```
\displaystyle
\frac{2\tan \frac{\pi}{6}}{1 - \tan^2\frac{\pi}{6}}
```

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0.26mins

Q5d

Determine the values of `\sin 2x, \cos 2x`

, and `\tan 2x`

, given

`\sin x =\dfrac{3}{5}`

, and `x`

is acute.

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2.00mins

Q6a

Determine the values of `\sin 2x, \cos 2x`

, and `\tan 2x`

, given

`\cot x = - \dfrac{7}{24}`

, and `x`

is obtuse.

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2.25mins

Q6b

Determine the values of `\sin 2x, \cos 2x`

, and `\tan 2x`

, given

`\cos x =\dfrac{12}{13}`

, and `\frac{3\pi}{2} \leq x \leq 2\pi `

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1.58mins

Q6c

Determine whether each of the following is a trigonometric equation or a trigonometric identity.

```
\displaystyle
\tan 2x = \frac{2\sin x\cos x}{1 -2\sin^2x}
```

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1.27mins

Q7a

Determine whether each of the following is a trigonometric equation or a trigonometric identity.

```
\displaystyle
\sec^2 x - \tan^2x = \cos x
```

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0.36mins

Q7b

Determine whether each of the following is a trigonometric equation or a trigonometric identity.

```
\displaystyle
\csc^2x -\cot^2x = \sin^2x + \cos^2x
```

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0.26mins

Q7c

Determine whether each of the following is a trigonometric equation or a trigonometric identity.

```
\displaystyle
\tan^2x = 1
```

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0.25mins

Q7d

Prove that ```
\displaystyle
\frac{1 - \sin^2x}{\cot^2x} = 1 -\cos^2x
```

is a trigonometric identity.

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1.19mins

Q8

Prove that ```
\displaystyle
\frac{2\sec^2x -2\tan^2 x}{\csc x} = \sin 2x\sec x
```

is a trigonometric identity.

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1.48mins

Q9

Solve for when `0 \leq x \leq 2\pi `

`\frac{2}{\sin x} + 10 = 6`

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0.44mins

Q10a

Solve for when `0 \leq x \leq 2\pi `

```
\displaystyle
-\frac{5\cot x}{2} + \frac{7}{3} = - \frac{1}{6}
```

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1.07mins

Q10b

Solve for when `0 \leq x \leq 2\pi `

```
\displaystyle
3 + 10 \sec x - 1 = -18
```

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0.48mins

Q10c

a) Solve the equation `y^2 - 4 = 0`

.

b) Solve `\csc^2x - 4 = 0`

in the interval `0 \leq x \leq 2\pi`

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1.09mins

Q11

Solve the equation for `x`

in the interval `0 \leq x \leq 2\pi`

```
\displaystyle
2\sin^2 x - \sin x - 1 =0
```

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0.46mins

Q12a

Solve the equation for `x`

in the interval `0 \leq x \leq 2\pi`

```
\displaystyle
\tan^2x \sin x - \frac{\sin x}{3} = 0
```

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1.01mins

Q12b

Solve the equation for `x`

in the interval `0 \leq x \leq 2\pi`

```
\displaystyle
\cos^2x + (\frac{1- \sqrt{2}}{2})\cos x - \frac{\sqrt{2}}{4} = 0
```

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1.32mins

Q12c

Solve the equation for `x`

in the interval `0 \leq x \leq 2\pi`

```
\displaystyle
25 \tan^2x - 70\tan x = -49
```

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1.33mins

Q12d

Solve the equation `\dfrac{1}{1 +\tan^2x} = -\cos x`

for `x`

in the interval `0 \leq x \leq 2\pi`

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1.15mins

Q13