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Solutions
22 Videos

Evaluate to four decimal places.

`\csc 20^o`

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Q1a

Evaluate to four decimal places.

`\cot 10^o`

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Q1b

Evaluate to four decimal places.

`\sec 75^o`

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Q1c

Evaluate to four decimal places.

`\csc 81^o`

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Q1d

Determine the value of `\theta`

to the nearest degree if `0^o\leq \theta \leq 90^o`

.

```
\displaystyle
\cot \theta = 0.8701
```

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Q2a

Determine the value of `\theta`

to the nearest degree if `0^o\leq \theta \leq 90^o`

.

```
\displaystyle
\sec \theta = 4.1011
```

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Q2b

Determine the value of `\theta`

to the nearest degree if `0^o\leq \theta \leq 90^o`

.

```
\displaystyle
\csc \theta = 1.6406
```

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Q2c

Determine the value of `\theta`

to the nearest degree if `0^o\leq \theta \leq 90^o`

.

```
\displaystyle
\sec \theta = 2.4312
```

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Q2d

A trigonometric ratio is `\frac{7}{5}`

. What ratio could it be, and what angle might it be referring to?

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Q3

Clark is attaching a rope to the top of the mast of her sailboat so that she can lower the sail to the ground to do some repairs. The mast is `8.3`

m long, and with her eyes level with the base of the mast, the top form an angle `31^o`

with the ground. How much rope does Claire need if `0.5`

m of rope is required tot tie to the mast? Round your answer to the nearest tenth of a metre.

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Q4

If `\csc \theta < \sec \theta`

and `\theta`

is acute, what do you know about `\theta`

?

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Q5

Determine the exact value of each trigonometric ratio.

```
\displaystyle
\begin{array}{ccccc}
&(a) \phantom{.} \sin 60^o &(a) \phantom{.} \csc 30^o \\
&(c) \phantom{.} \tan 45^o &(d) \phantom{.} \sec 45^o
\end{array}
```

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Q6

Given `\triangle ABC`

as shown,

a) determine the exact measure of each unknown side if `\sin \alpha = \frac{1}{2}`

.

b) determine the exact values of the primary trigonometric ratios for `\angle A`

and `\angle DBC`

.

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Q7

i) Sketch each angle in standard position. Use the sketch to determine the exact value of the given trigonometric ratio.

ii) If `0^o \leq \theta \leq 360^o`

, state all values of \theta that have the same given trigonometric ratio.

`\sin 120^o`

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Q8a

i) Sketch each angle in standard position. Use the sketch to determine the exact value of the given trigonometric ratio.

ii) If `0^o \leq \theta \leq 360^o`

, state all values of \theta that have the same given trigonometric ratio.

`\cos 225^o`

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Q8b

i) Sketch each angle in standard position. Use the sketch to determine the exact value of the given trigonometric ratio.

ii) If `0^o \leq \theta \leq 360^o`

, state all values of \theta that have the same given trigonometric ratio.

`\tan 330^o`

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Q8c

`0^o \leq \theta \leq 360^o`

, state all values of \theta that have the same given trigonometric ratio.

`\cos 300^o`

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Q8d

`P(-9, 4)`

lies on the terminal arm of an angle in standard position.

a) Sketch the principal angle \theta.

b) What is the value of the related acute angle `\beta`

to the nearest degree?

c) What is the value of the principal angle `\theta`

to the nearest degree?

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Q9

Is it possible that `\cos \theta = \frac{4}{5}`

has 3 different answer when `0^o \leq \theta \leq 360^o`

? Explain. If not, how many answer can it have?

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Q10

Given `\tan \theta = -\frac{15}{8}`

, where `90^o \leq \theta \leq 180^o`

,

a) state the other five trigonometric ratios as fractions.

b) determine the value of `\theta`

to the nearest degree.

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Q11

If `\sin \theta = -0.8190`

and `0^o \leq \theta \leq 360^o`

, determine the value of `\theta`

to the nearest degree.

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Q12

\theta lies in quadrant II. Without using a calculator, which ratios must be false? Justify your reasoning.

a) `\cos \theta = 2.3151`

b) `\tan \theta = 2.3151`

c) `\sec \theta = 2.3151`

d) `\csc \theta = 2.3151`

e) `\cot \theta = 2.3151`

f) `\sin \theta = 2.3151`

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Q13