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Solutions
24 Videos

- i) For each triangle, state the reciprocal trigonometric ratios for angle
`\theta`

. - ii) Calculate the value of
`\theta`

to the nearest degree.

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1.24mins

Q1a

- i) For each triangle, state the reciprocal trigonometric ratios for angle
`\theta`

. - ii) Calculate the value of
`\theta`

to the nearest degree.

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1.20mins

Q1b

- i) For each triangle, state the reciprocal trigonometric ratios for angle
`\theta`

. - ii) Calculate the value of
`\theta`

to the nearest degree.

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1.10mins

Q1c

- i) State the sign of each trigonometric ratio. Use a calculator to determine the value of each ratio.
- ii) For each trigonometric ratio, determine the principal angle and, where appropriate, the related acute angle. Then sketch another angle that has the equivalent ratio. Label the principal angle and the related acute angle on your sketch.

```
\displaystyle
\tan (18^o)
```

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0.23mins

Q3a

- i) State the sign of each trigonometric ratio. Use a calculator to determine the value of each ratio.
- ii) For each trigonometric ratio, determine the principal angle and, where appropriate, the related acute angle. Then sketch another angle that has the equivalent ratio. Label the principal angle and the related acute angle on your sketch.

```
\displaystyle
\sin (205^o)
```

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0.19mins

Q3b

i) State the sign of each trigonometric ratio. Use a calculator to determine the value of each ratio.

ii) For each trigonometric ratio, determine the principal angle and, where appropriate, the related acute angle. Then sketch another angle that has the equivalent ratio. Label the principal angle and the related acute angle on your sketch.

```
\cos(-55^o)
```

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0.36mins

Q3c

For each sketch, state the primary trigonometric ratios associated with angle `\theta`

. Express your answers in simplified radical form.

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0.43mins

Q4a

`\theta`

. Express your answers in simplified radical form.

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0.53mins

Q4b

`\theta`

. Express your answers in simplified radical form.

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0.37mins

Q4c

Given `\cos \phi = -\frac{7}{\sqrt{53}}`

, where `0^{\circ} \leq \phi \leq 360^{\circ}`

**(a)** in which quadrant(s) does the terminal arm of angle `\phi`

lie? Justify your answer.

**(b)** state the other five trigonometric ratios for angle `\phi`

.

**(c)** calculate the value of the principal angle `\phi`

to the nearest degree.

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3.09mins

Q5

Determine whether the equation `\cos \beta \cot \beta = \frac{1}{\sin \beta} - \sin \beta`

is an identity. State any restrictors on angle `\beta`

.

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2.14mins

Q6

Prove the identity. State any restrictions on the variables if all angles vary from `0^{\circ}`

to `360^{\circ}`

.

`\tan \alpha \cos \alpha = \sin \alpha`

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0.15mins

Q7a

Prove the identity. State any restrictions on the variables if all angles vary from `0^{\circ}`

to `360^{\circ}`

.

`\frac{1}{\cot \phi} = \sin \phi \sec \phi `

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0.31mins

Q7b

Prove the identity. State any restrictions on the variables if all angles vary from `0^{\circ}`

to `360^{\circ}`

.

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

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1.30mins

Q7c

`0^{\circ}`

to `360^{\circ}`

.

`\sec \theta\cos \theta + \sec \theta \sin \theta = 1 + \tan \theta`

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0.26mins

Q7d

Determine whether it is possible to draw a triangle given each set of information. Sketch all possible triangles where appropriate. Calculate, then label, all side lengths to the nearest tenth of ta centimetre and all angles to the nearest degree.

`b = 3.0 cm, c = 5.5 cm, \angle B = 30^{\circ}`

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3.56mins

Q8a

Determine whether it is possible to draw a triangle given each set of information. Sketch all possible triangles where appropriate. Calculate, then label, all side lengths to the nearest tenth of ta centimetre and all angles to the nearest degree.

`b = 12.1 cm, c = 8.2 cm, \angle C = 34^{\circ}`

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4.47mins

Q8b

Determine whether it is possible to draw a triangle given each set of information. Sketch all possible triangles where appropriate. Calculate, then label, all side lengths to the nearest tenth of ta centimetre and all angles to the nearest degree.

`a = 11.1 cm, c = 5.2 cm, \angle C = 33^{\circ}`

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1.11mins

Q8c

Two forest fire stations, P and Q, are 20.0 km apart. A ranger at station Q sees a fire 15.0 km away. If the angle between the line PQ and the line from P to the fire is `25^{\circ}`

, how far, to the nearest tenth of a kilometre, is station P from the fire?

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3.11mins

Q9

Determine each unknown side length to the nearest tenth.

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0.32mins

Q10a

Determine each unknown side length to the nearest tenth.

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0.24mins

Q10b

Two spotlights, one blue and the other white, are placed `6.0 m`

apart on a track on the ceiling of a ballroom. A stationary observer standing on the ballroom floor notices that the angle of elevation is `45^{o}`

to the blue spotlight and `70^{o}`

to the white one. How high, to the nearest tenth of a metre, is the ceiling of the ballroom?

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2.08mins

Q11

To determine the height of a pole across a road, Justin takes two measurements. He stands at point A directly across from the base of the pole and determine that the angle of elevation to the top of the pole is `15.3^{o}`

. He then walks 30 m parallel to the freeway to point C, where he sees that the base of the pole and point A are `57.5^{o}`

apart. From point A, the base of the pole and point C are `90.0^{o}`

apart. Calculate the height of the pole to the nearest metre.

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1.25mins

Q12