- #1
huntingrdr
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Homework Statement
Find all values of x in the interval [0,2pi] that satisfy the inequality.
sin x > cos x
Homework Equations
Unit circle
The Attempt at a Solution
pi/3 > x > 7pi/6
Is that correct?
Mark44 said:No, and no. pi/3 is not larger than 7pi/6, and neither value is correct for sin x = cos x. You need to find all solutions of this equation in the interval [0, 2pi], and then find the intervals for which sin x > cos x.
This is your problem, and is what Char. limit and I have been trying to get across to you. In order to find out where sin x > cos x, you need to first find out where sin x = cos x. There are two values of x in [0, 2pi] that satisfy this equation. The interval you specify for which sin x > cos x will have to use these values.huntingrdr said:I am not trying to find where sinx = cosx.
It is not true that sinx = cosx at all of these values. Some of them, yes, but not all of them.huntingrdr said:I know pi/4, 3pi/4, 5pi/4, and 7pi/4: sinx=cosx though.
pi/3 and 7pi/6 are totally irrelevant to this problem.huntingrdr said:Ok I'm not sure how to write it in inequality format but I know starting at pi/3 and going to 7pi/6, the sinx value is great than the cosx value. Right? Now how can I write this in inequality notation?
Maybe it is 7pi/6 > x > pi/3
A unit circle is a circle with a radius of 1 unit. It is often used in mathematics to simplify calculations involving angles and trigonometric functions.
To find x satisfying sin x > cos x on the unit circle, you can use the Pythagorean identity sin^2x + cos^2x = 1. This means that when sin x > cos x, sin^2x will be greater than cos^2x, and therefore x will be located in the first and second quadrants of the unit circle where sin x is greater than cos x.
Yes, you can use a calculator to find x satisfying sin x > cos x on the unit circle. You can use the inverse sine function (sin^-1) to find the angle whose sine is greater than its cosine. Make sure your calculator is in degree mode if you are working with degrees.
Yes, there are multiple solutions for x satisfying sin x > cos x on the unit circle. Since sin x and cos x are periodic functions, there will be infinite solutions for x satisfying this inequality. The solutions will be in the form of x = 90° + n(360°), where n is an integer.
The unit circle is closely related to trigonometry. The coordinates of any point on the unit circle can be represented as (cos x, sin x), where x is the angle formed by the radius of the circle and the positive x-axis. This relationship allows us to use the unit circle to easily calculate trigonometric ratios for any angle.