osafi52 said:Consider two trigonometric functions y = cos 2x and y = 1 + sinx.(a) Write down the equation in x that you would solve to find the x coordinate of point(s) of intersection of those graphs on [0, 2∏].
(b) Solve your equation, and write down the coordinates of the point(s) of intersection .
osafi52 said:thanks so much for the reply it really helped.once i solved the equation i got x=0 and x= 30 .
Hi. thanks for the reply. i solved the equation and got x =0 and x=-30. firstly is this correct and does this answer the question b.greg1313 said:(a) $\cos(2x)=1+\sin(x)$
(b) $\cos(2x)=1-2\sin^2(x)=1+\sin(x)$
$2\sin^2(x)+\sin(x)=0$
$\sin(x)(2\sin(x)+1)=0$
Can you finish?
skeeter said:\(\displaystyle \sin(x) = 0\) at \(\displaystyle x = 0^\circ\) and \(\displaystyle x = 180^\circ\) for $0^\circ \le x < 360^\circ$
\(\displaystyle 2\sin(x)+1 = 0 \implies \sin(x) = -\dfrac{1}{2}\) ... you want to try to find the degree solutions for $x$ again?
osafi52 said:thanks for that. 2sinx+1=0 should have got x=-30.
The intersection of two equations refers to the point or points where the two lines or curves represented by the equations meet or cross each other.
To find the intersection of two equations, you can use a variety of methods such as graphing, substitution, or elimination. Graphing involves plotting both equations on the same graph and finding the point where they intersect. Substitution involves solving one equation for a variable and plugging it into the other equation to find the point of intersection. Elimination involves manipulating the equations to eliminate one variable and then solving for the other variable.
If two equations have no intersection, it means the lines or curves represented by the equations do not intersect each other. This could happen if the equations represent parallel lines or if they represent two curves that do not cross each other.
Yes, two equations can have more than one intersection. This occurs when the equations represent two curves that intersect at more than one point, such as a circle and a line.
The intersection of two equations has many applications in real life, such as in solving systems of equations to find the optimal solution for a business problem, determining the break-even point for a company, or finding the point of intersection between supply and demand curves in economics. It can also be used in engineering and physics to find the point where two objects or forces intersect.