- #1
meatandpotatoes22003
- 3
- 0
Can someone break down in "baby steps" how to solve the following?:
cos7pi/6=?
thank you.
cos7pi/6=?
thank you.
How to solve cos7pi/6 in baby steps?
- Context: High School
- Thread starter meatandpotatoes22003
- Start date
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- Tags
- Precalculus Trigonometry
Click For Summary
Discussion Overview
The discussion focuses on finding the value of cos(7π/6) through various methods, including geometric interpretations and trigonometric identities. Participants explore the concept in a step-by-step manner, considering both theoretical and practical approaches.
Discussion Character
- Exploratory
- Technical explanation
- Mathematical reasoning
- Homework-related
Main Points Raised
- Some participants suggest using the CAST quadrant diagram or the cos(A+B) formula, noting that these methods require knowledge of cos(π/6) = (√3)/2.
- One participant explains the relationship between radians and degrees, indicating that π radians corresponds to 180 degrees, and thus 7π/6 represents an additional 30 degrees beyond 6π/6.
- Another participant describes the cosine of 6π/6 as -1, leading to the conclusion that cos(7π/6) involves a triangle with a 30-degree angle positioned along the negative x-axis.
- There is a suggestion to use the identity cos(π + α) = -cos(α) to simplify the calculation.
- Participants discuss the implications of the triangle's orientation on the sign of the cosine value, indicating that the cosine will be negative due to the triangle being drawn in the third quadrant.
Areas of Agreement / Disagreement
Participants present multiple methods and interpretations for solving cos(7π/6), leading to a lack of consensus on the preferred approach. Disagreement exists regarding the best way to visualize and calculate the cosine value.
Contextual Notes
Some assumptions about the understanding of trigonometric identities and the relationship between radians and degrees are present. The discussion does not resolve the mathematical steps involved in calculating cos(7π/6).
Who May Find This Useful
Readers interested in trigonometry, particularly those seeking to understand cosine values in different quadrants and the application of trigonometric identities.
- #2
Gaz031
- 51
- 0
You can either use the CAST quadrant diagram or the cos(A+B) formulae, but both rely on you knowing cos(pi/6)=(rt3)/2meatandpotatoes22003 said:Can someone break down in "baby steps" how to solve the following?:
cos7pi/6=?
thank you.
- #3
SteveRives
- 56
- 0
Q. How many times does pi go into a circle?
A. Two times. And that is the same as going 360 degress.
Q. Then half a circle is has one pi?
A. Right.
Q. So pi is like 180 degrees?
A. Right, and Cos of 180 degress is Cos 6pi/6. And that is like having a trinangle that has no opposite edge. Such a triangle is not much of a triangle, O / H is zero.
Q. So what is Cos 6pi/6?
A. It is A/H where A and H are the same lenght, only we are going in a negative direction for A (relative to the X axis).
Q. That means Cos 6pi/6 is -1?
A. That's right.
Q. Okay, that takes care of Cos 6pi/6, what about Cos 7pi/6?
A. Well, that's like going 1/6th of pi (where pi is 180 degrees) farther than we already have. We've gone 6pi/6 to sweep half a circle, now we go a little more beyond that.
Q. So that would be 30 degrees more, right?
A. Right, becasue six times 30 is 180, and we want 1/6th more of that; so we go the extra 30 degrees to make 7/6th of pi.
Q. So we are talking about a triangle with a 30 degree angle?
A. That's right, and it is drawn along the negative x-axis below it.
Q. So how do I find Cos 30 degrees?
A. You can draw a 30 degree triangle with a protractor and measure the ratio of A/H.
Q. So will it be positive or negative?
A. Even though it is a 30 dgree triangle, it has been layed along the X axis on the negative side. So A will be negative in the A/H ratio.
A. Two times. And that is the same as going 360 degress.
Q. Then half a circle is has one pi?
A. Right.
Q. So pi is like 180 degrees?
A. Right, and Cos of 180 degress is Cos 6pi/6. And that is like having a trinangle that has no opposite edge. Such a triangle is not much of a triangle, O / H is zero.
Q. So what is Cos 6pi/6?
A. It is A/H where A and H are the same lenght, only we are going in a negative direction for A (relative to the X axis).
Q. That means Cos 6pi/6 is -1?
A. That's right.
Q. Okay, that takes care of Cos 6pi/6, what about Cos 7pi/6?
A. Well, that's like going 1/6th of pi (where pi is 180 degrees) farther than we already have. We've gone 6pi/6 to sweep half a circle, now we go a little more beyond that.
Q. So that would be 30 degrees more, right?
A. Right, becasue six times 30 is 180, and we want 1/6th more of that; so we go the extra 30 degrees to make 7/6th of pi.
Q. So we are talking about a triangle with a 30 degree angle?
A. That's right, and it is drawn along the negative x-axis below it.
Q. So how do I find Cos 30 degrees?
A. You can draw a 30 degree triangle with a protractor and measure the ratio of A/H.
Q. So will it be positive or negative?
A. Even though it is a 30 dgree triangle, it has been layed along the X axis on the negative side. So A will be negative in the A/H ratio.
- #4
mathwonk
Science Advisor
Homework Helper
- 12,000
- 2,307
look at a circle. and find 7pi/6. then ask what the coordinates of that point are.
- #5
VietDao29
Homework Helper
- 1,424
- 3
Why don't you use:
[tex]\cos(\pi + \alpha) = -\cos{\alpha}[/tex]
Viet Dao,
[tex]\cos(\pi + \alpha) = -\cos{\alpha}[/tex]
Viet Dao,
Last edited:
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