- #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
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SUMMARY
The discussion focuses on solving the trigonometric expression cos(7π/6) using fundamental concepts of the unit circle and trigonometric identities. The solution involves recognizing that 7π/6 is located in the third quadrant, where cosine values are negative. By understanding that cos(6π/6) equals -1 and that cos(30°) equals √3/2, the final result is derived as cos(7π/6) = -√3/2. The discussion emphasizes the importance of visualizing angles on the unit circle and applying the cosine addition formula.
PREREQUISITES- Understanding of the unit circle and quadrants
- Knowledge of basic trigonometric functions, specifically cosine
- Familiarity with the cosine addition formula
- Ability to convert between radians and degrees
- Study the unit circle and its applications in trigonometry
- Learn how to use the cosine addition formula in various contexts
- Explore the properties of trigonometric functions in different quadrants
- Practice converting between radians and degrees for various angles
Students learning trigonometry, educators teaching trigonometric concepts, and anyone seeking to improve their understanding of angles and cosine functions in mathematics.
- #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
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- 2,240
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:
\cos(\pi + \alpha) = -\cos{\alpha}
Viet Dao,
\cos(\pi + \alpha) = -\cos{\alpha}
Viet Dao,
Last edited:
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