Not understanding trig problem

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Homework Help Overview

The discussion revolves around a trigonometric problem involving angles, specifically angle AOP and angle AOG, and their relationships as a line revolves from the positive y-axis. Participants are trying to clarify the definitions and measurements of these angles in the context of standard trigonometric conventions.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the relationship between angles AOP and AOG, particularly whether AOG should be considered as 90 - theta or 90 + theta. There is also discussion about the implications of measuring angles clockwise versus counter-clockwise.

Discussion Status

The discussion is ongoing, with participants seeking to understand the correct interpretation of angle measurements. Some guidance has been provided regarding standard definitions of angles, but there is no explicit consensus on the correct relationship between the angles at this point.

Contextual Notes

There is mention of a diagram from a book that may not align with standard definitions, which could be contributing to the confusion. The discussion also highlights the importance of the reference direction for angle measurements in trigonometry.

Miike012
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angle AOP is theta..
let the revolving line start on the pos y-axis and revolve through the angle theta in clock wise direction.
the angle AOG is then 90 - theta..

I don't understand how angle AOG is 90 - theta.. it lookes like 90 + theta to me...?
 

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AOG is a negative angle.
 
Ok... so what does that mean? how does that mean it is 90 - theta?
 
Is the picture you show directly from your book? If so then that formula is NOT correct. You show the angle measured from the positive y-axis but ask about angle AOP when A is on the x-axis.

The standard definition for angles is that positive angles are measured counter-clockwise from the positive x-axis, negative angles are measured clockwise. Let's say that the line OP is "x" degrees below line OA and that OG is "x" degrees to the left of the vertical line. Taking line OAG to be measured clockwise from the positive x-axis, NOT the positive y-axis as shown, the measure of OAG is -(270-x)= -270+ x degrees. The measure of AOP is theta= 360- x. 90- theta= 90-(360- x)= -270+ x
 

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