Points of intersection

[mikeyrobert]

Hello, i need help with finding the points of intersection f(x)=sin^3(x)+cos^3(x). Point of intersection with Y axis is 1, but i don't know how to solve sin^3(x)+cos^3(x)=0 to get the points on X axis. Thank you for help.

 

[Deleted member 4993]

Hello, i need help with finding the points of intersection f(x)=sin^3(x)+cos^3(x). Point of intersection with Y axis is 1, but i don't know how to solve sin^3(x)+cos^3(x)=0 to get the points on X axis. Thank you for help.

Use

a³ + b³ = (a + b)(a² - ab + b²)

 

[HallsofIvy]

Equivalently, if \(\displaystyle a^3+ b^3= 0\) then \(\displaystyle a^3= -b^3\). The only (real number) solutions to that satisfy a= -b.