Question

How cos(180_80) become -cos180

Answer 1

first of all do you know the ASTC rule in trigonometry if no listen

there are 4 quadrants in XY plane the first quadrant lies between 0 and 90 degrees here all trigonometric functions are positive that is sin,cos,tan,sec,cosecant ,cot in second quadrant lies between 90 and 180 degrees here sin and cosec are positive rest are negative in third quadrant lies between 180 and 270 degrees here tan and cot are positive rest of them are negative similarly in the fourth quadrant which lies between 270 and 360 degrees here cos and tan are positive

now to your question

cos (180-80) which means the the angle becoming less than 180 which means it lies in second quadrant

where cos is negative

there is a formula

cos( pi-x)=-cosx