That certainly is NOT true! What is sin(pi)+ cos(pi)? Look at the signs of sin(pix)+ cos(pix)- x at 0 and 1.skateza said:Homework Statement
Show that x=sin(piex) + cos(piex) has a solution in [0,-1]
The Attempt at a Solution
well i know that 0 <= x <= 1
therefore 0 <= sin(piex) + cos(piex) <= 1
But how do i go about solving this inequality?
A trigonometric inequality is an inequality that involves trigonometric functions, such as sine, cosine, and tangent. These inequalities can be solved using algebraic techniques and the properties of trigonometric functions.
The solution to a trigonometric inequality in the interval [0,-1] is the set of all values of the variable that satisfy the inequality. This means that any value within the interval that makes the inequality true is part of the solution set.
To solve a trigonometric inequality in the interval [0,-1], you can use algebraic techniques such as factoring and the properties of trigonometric functions. You will also need to use knowledge of the unit circle and the periodic nature of trigonometric functions.
Finding the solution to a trigonometric inequality in the interval [0,-1] can help you determine the range of values for a variable that will make the inequality true. This can be useful in various applications, such as optimizing a function or solving real-world problems involving angles or triangles.
Yes, a trigonometric inequality in the interval [0,-1] can have multiple solutions. This is because trigonometric functions are periodic and have an infinite number of solutions. For example, the inequality sinx > 0 in the interval [0,-1] has infinitely many solutions, as sine is positive in all quadrants of the unit circle.