TRIGONOMETRY - Angles Trigonometry began as a study of the right triangle. It was discovered that certain relationships between the sides of the right.

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Presentation transcript:

TRIGONOMETRY - Angles Trigonometry began as a study of the right triangle. It was discovered that certain relationships between the sides of the right triangle could be used to find the measurement of the angles in the given triangle. Trigonometry has expanded into technology and is used to describe radio and television waves and is used by the military in sonar and sniper applications.

TRIGONOMETRY - Angles Trigonometry began as a study of the right triangle. It was discovered that certain relationships between the sides of the right triangle could be used to find the measurement of the angles in the given triangle. Trigonometry has expanded into technology and is used to describe radio and television waves and is used by the military in sonar and sniper applications. To begin, we need to identify some parameters.

TRIGONOMETRY - Angles Trigonometry began as a study of the right triangle. It was discovered that certain relationships between the sides of the right triangle could be used to find the measurement of the angles in the given triangle. Trigonometry has expanded into technology and is used to describe radio and television waves and is used by the military in sonar and sniper applications. To begin, we need to identify some parameters. Θ – the Greek letter theta, used to identify ( name ) an angle

TRIGONOMETRY - Angles Trigonometry began as a study of the right triangle. It was discovered that certain relationships between the sides of the right triangle could be used to find the measurement of the angles in the given triangle. Trigonometry has expanded into technology and is used to describe radio and television waves and is used by the military in sonar and sniper applications. To begin, we need to identify some parameters. Θ – the Greek letter theta, used to identify ( name ) an angle Initial side – where the angle starts ( usually the + side of the x – axis ) Terminal side – where the angle ends Initial side Terminal side θ

TRIGONOMETRY - Angles Trigonometry began as a study of the right triangle. It was discovered that certain relationships between the sides of the right triangle could be used to find the measurement of the angles in the given triangle. Trigonometry has expanded into technology and is used to describe radio and television waves and is used by the military in sonar and sniper applications. To begin, we need to identify some parameters. Θ – the Greek letter theta, used to identify ( name ) an angle Initial side – where the angle starts ( usually the + side of the x – axis ) Terminal side – where the angle ends Vertex – where the initial and terminal sides meet Initial side Terminal side θ vertex

TRIGONOMETRY - Angles Trigonometry began as a study of the right triangle. It was discovered that certain relationships between the sides of the right triangle could be used to find the measurement of the angles in the given triangle. Trigonometry has expanded into technology and is used to describe radio and television waves and is used by the military in sonar and sniper applications. If an angle is measured counterclockwise, it is a POSITIVE angle Initial side Terminal side θ

TRIGONOMETRY - Angles Trigonometry began as a study of the right triangle. It was discovered that certain relationships between the sides of the right triangle could be used to find the measurement of the angles in the given triangle. Trigonometry has expanded into technology and is used to describe radio and television waves and is used by the military in sonar and sniper applications. If an angle is measured counterclockwise, it is a POSITIVE angle If an angle is measured clockwise, it is a NEGATIVE angle Initial side Terminal side θ

TRIGONOMETRY - Angles Conventional geometric measure of an angle is done in degrees. Trigonometry uses radians to measure angles. Since we are rotating a terminal side away from an initial side around a vertex ( center ), radian measure is based on a circle with a radius of 1.

TRIGONOMETRY - Angles Conventional geometric measure of an angle is done in degrees. Trigonometry uses radians to measure angles. Since we are rotating a terminal side away from an initial side around a vertex ( center ), radian measure is based on a circle with a radius of 1. Circle = 360 ⁰ 1

TRIGONOMETRY - Angles Conventional geometric measure of an angle is done in degrees. Trigonometry uses radians to measure angles. Since we are rotating a terminal side away from an initial side around a vertex ( center ), radian measure is based on a circle with a radius of 1. Circle = 360 ⁰ 1 θ

TRIGONOMETRY - Angles Conventional geometric measure of an angle is done in degrees. Trigonometry uses radians to measure angles. Since we are rotating a terminal side away from an initial side around a vertex ( center ), radian measure is based on a circle with a radius of 1. Circle = 360 ⁰ 1 θ

TRIGONOMETRY - Angles Being able to convert from degrees to radians ( and vice versa ) will be critical. Below are the formulas for each type. Degrees to radians : Radians to degrees :

TRIGONOMETRY - Angles Being able to convert from degrees to radians ( and vice versa ) will be critical. Below are the formulas for each type. Degrees to radians : Radians to degrees : EXAMPLE # 1 : Convert 80 ⁰ to radians

TRIGONOMETRY - Angles Being able to convert from degrees to radians ( and vice versa ) will be critical. Below are the formulas for each type. Degrees to radians : Radians to degrees : EXAMPLE # 1 : Convert 80 ⁰ to radians

TRIGONOMETRY - Angles Being able to convert from degrees to radians ( and vice versa ) will be critical. Below are the formulas for each type. Degrees to radians : Radians to degrees : EXAMPLE # 1 : Convert 80 ⁰ to radians

TRIGONOMETRY - Angles Being able to convert from degrees to radians ( and vice versa ) will be critical. Below are the formulas for each type. Degrees to radians : Radians to degrees : EXAMPLE # 1 : Convert 80 ⁰ to radians