## Trigonometry Math Worksheet – Basics of Angles

March 8, 2012 in Additional Mathematics, Basic Angles, Trigonometry, Trigonometry Worksheet by Shivakkumar Vadiveyl

## Trigonometry Math Worksheet – Basics of Angles

1) Write the values of the angles for the below graph.

Trigonometry – Positive Angles 5

2) Write the values of the angles for the below graph.

Trigonometry – Negative Angles 2

3) Draw the angles for these values in a graph and indicate clearly the angles and its direction.

$0^{circ},,,160^{circ},,,260^{circ},,,360^{circ},,,45^{circ}$

4) Draw the angles for these values in a graph and indicate clearly the angles and its direction.

$0^{circ},,,-135^{circ},,,-250^{circ},,,-360^{circ},,,-30^{circ}$

Trigonometry – Basics of Angles Math Worksheet Answers

1) Write the values of the angles for the below graph.

Trigonometry – Positive Angles 5

$begin{array}{ccccc}& 40^{circ}, & 200^{circ}end{array}$

2) Write the values of the angles for the below graph.

Trigonometry – Negative Angles 2

$begin{array}{ccccc}& -35^{circ}, & -160^{circ}end{array}$

3) Draw the angles for these values in a graph and indicate clearly the angles and its direction.

$0^{circ},,,160^{circ},,,260^{circ},,,360^{circ},,,45^{circ}$

Trigonometry – Positive Angles 6

4) Draw the angles for these values in a graph and indicate clearly the angles and its direction.

$0^{circ},,,-135^{circ},,,-250^{circ},,,-360^{circ},,,-30^{circ}$

Trigonometry – Negative Angles 5

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## Trigonometry I – Basics of Angles

March 8, 2012 in Additional Mathematics, Basic Angles, Trigonometry by Shivakkumar Vadiveyl

## Trigonometry – Basics of Angles

The study of trigonometry is study of angles. Trigonometry is used extensively in engineering and physics. Navigational systems use trigonometry to chart the course of ships and aircrafts.

This below chart is the very basic representation of an angle in the Cartesian plane. The angle is commonly denoted by Greek letters such as theta, $theta$, alpha, $alpha$ and beta, $beta$.

The angle is made by a ray that originates from the (0,0) coordinate and moves from the x-axis in either clockwise or counter-clockwise direction.

Trigonometry - Basic Angles

Positive Angles

In this diagram, the angle $theta$ is drawn in the counter-clockwise direction and is a positive angle. In the angle is made by the ray that is travelling in clockwise direction, the sign of the angle would be negative.

Trigonometry - Positive Angles

Here are some examples of positive angles and how it is drawn.

The positive x-axis is $0^{circ}$, the positive y-axis is $90^{circ}$, the negative x-axis is $180^{circ}$ and the negative y-axis is $270^{circ}$.

Trigonometry - Positive Angles 2

If the ray completes one revolution and returns back to the positive x-axis, the positive x-axis then becomes $360^{circ}$ as well. One revolution is $360^{circ}$. The angle can be larger than $360^{circ}$ and it increases as the ray continously moves in a circular motion.

Here are futher examples of positive angles.

Trigonometry - Positive Angles 3

Negative Angles

If the ray moves in the clockwise direction, the angle that is formed is a negative angle as depicted in the below graph.

Trigonometry - Negative Angles

The positive x-axis is $0^{circ}$, the negative y-axis is $-90^{circ}$, the negative x-axis is $180^{circ}$ and the positive y-axis is $-270^{circ}$.

Trigonometry - Negative Angles 1

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