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Solutions
37 Videos

Convert each angle from radians to degrees. Express your answer to one decimal place, if necessary.

```
\displaystyle
\frac{\pi}{8}
```

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Q1a

Convert each angle from radians to degrees. Express your answer to one decimal place, if necessary.

```
\displaystyle
4\pi
```

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Q1b

Convert each angle from radians to degrees. Express your answer to one decimal place, if necessary.

```
\displaystyle
5
```

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Q1c

Convert each angle from radians to degrees. Express your answer to one decimal place, if necessary.

```
\displaystyle
\frac{11\pi}{12}
```

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Q1d

Convert each angle from degrees to radians. Express your answer to one decimal place, if necessary.

```
\displaystyle
125^o
```

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Q2a

Convert each angle from degrees to radians. Express your answer to one decimal place, if necessary.

```
\displaystyle
450^o
```

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Q2b

Convert each angle from degrees to radians. Express your answer to one decimal place, if necessary.

```
\displaystyle
5^o
```

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Q2c

Convert each angle from degrees to radians. Express your answer to one decimal place, if necessary.

```
\displaystyle
330^o
```

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Q2d

Convert each angle from degrees to radians. Express your answer to one decimal place, if necessary.

```
\displaystyle
215^o
```

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Q2e

Convert each angle from degrees to radians. Express your answer to one decimal place, if necessary.

```
\displaystyle
5^o
```

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Q2f

A tire with a diameter of 38 cm rotates 10 times in 5 s.

a) What is the angle that the tire rotates through, in radians, from 0 s to 5 s?

b) Determine the angular velocity of the tire.

c) Determine the distance travelled by a pebble that is trapped in the tread of the tire.

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Q3

Sketch each angle in standard position, and then determine the exact value of the trigonometric ratio.

```
\displaystyle
\sin \frac{3\pi}{4}
```

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Q4a

Sketch each angle in standard position, and then determine the exact value of the trigonometric ratio.

```
\displaystyle
\sin \frac{11\pi}{6}
```

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Q4b

Sketch each angle in standard position, and then determine the exact value of the trigonometric ratio.

```
\displaystyle
\tan \frac{5\pi}{3}
```

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Q4c

```
\displaystyle
\tan \frac{5\pi}{6}
```

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Q4d

```
\displaystyle
\cos \frac{3\pi}{2}
```

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Q4e

```
\displaystyle
\cos \frac{4\pi}{3}
```

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Q4f

The terminal arms of angles in standard position pass through the following points. Find the measure of each angle in radians, to the nearest hundredth.

`(-3, 14)`

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Q5a

The terminal arms of angles in standard position pass through the following points. Find the measure of each angle in radians, to the nearest hundredth.

`(6, 7)`

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Q5b

The terminal arms of angles in standard position pass through the following points. Find the measure of each angle in radians, to the nearest hundredth.

`(1, 9)`

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Q5c

`(-5, -18)`

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Q5d

`(2, 3)`

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Q5e

`(4, -20)`

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Q5f

```
\displaystyle
\sin (- \frac{7\pi}{6})
```

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Q6a

```
\displaystyle
\cot ( \frac{7\pi}{4})
```

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Q6b

```
\displaystyle
\sec ( -\frac{\pi}{2})
```

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Q6c

```
\displaystyle
\cos ( -\frac{5\pi}{6})
```

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Q6d

State the x-intercepts and y-intercepts of the graph of the following functions.

```
\displaystyle
y = \sin x
```

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Q7a

State the x-intercepts and y-intercepts of the graph of the following functions.

```
\displaystyle
y = \cos x
```

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Q7b

State the x-intercepts and y-intercepts of the graph of the following functions.

State the x-intercepts and y-intercepts of the graph of the following functions.

```
\displaystyle
y = \tan x
```

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Q7c

Sketch the graph of each function on the interval ```
\displaystyle
-2\pi \leq x \leq 2\pi
```

.

`y = \tan x`

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Q8a

Sketch the graph of each function on the interval ```
\displaystyle
-2\pi \leq x \leq 2\pi
```

.

```
\displaystyle
y = 2\sin(-x) - 1
```

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Q8b

Sketch the graph of each function on the interval ```
\displaystyle
-2\pi \leq x \leq 2\pi
```

.

```
\displaystyle
y =\frac{5}{2} \cos(2(x + \frac{\pi}{4})) + 3
```

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Q8c

Sketch the graph of each function on the interval ```
\displaystyle
-2\pi \leq x \leq 2\pi
```

.

```
\displaystyle
y = - \frac{1}{2} \cos(\frac{1}{2}x - \frac{\pi}{6})
```

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Q8d

Sketch the graph of each function on the interval ```
\displaystyle
-2\pi \leq x \leq 2\pi
```

.

```
\displaystyle
y = 2\sin(-(x - \frac{\pi}{2}))+ 4
```

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Q8e

Sketch the graph of each function on the interval ```
\displaystyle
-2\pi \leq x \leq 2\pi
```

.

```
\displaystyle
y = 0.4 \sin(\pi - 2x) - 2.5
```

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Q8f