Course and coarse are homophones, and consequently, easily confused words. The spell-check application in word-processing software wouldn’t catch a slip-up with these words because they are both words that are spelled correctly.
Course is a noun, referring to a path or other track to be followed beginning to end. It also applies to classes a student takes at school or other training. A popular idiom, borrowed from golf, says ” <<something>> is par for the course;” this means that the subject is part of the process and to be expected, although it’s challenge and a problem for the person experiencing it.
Coarse is an adjective. It describes a rough, or rippled (not smooth) texture. For instance, naturally dark brown and black hair is very coarse compared to naturally blonde hair, which has fine, thin strands. Let’s just say I know coarse hair firsthand. In another example, burlap is a coarse fabric, especially compared to silk to satin.
In conclusion the following sentence uses both words correctly:
At cosmetology school, Velma enrolled in a course that focused on challenges with straight and coarse hair.