Integration (1 Viewer)

[Lima_bosty]

hey guys how would i integrate this keeping the answer in exact value.



I got up to subbing the values and cant seem to figure out the exact when subbing pie/4.

 

[Aeonium]

 

[Lima_bosty]

thank you, but how did you figure that cos 3pie/4 = -root 2/2

 

[liamkk112]

thank you, but how did you figure that cos 3pie/4 = -root 2/2

plug into claculator
or:
cos pi/4 = root(2)/2
cos (pi - pi/4) = -cos(pi/4) (cos is taking in the acute angle pi/4, but now in quadrant 2, where only sin is positive)
thus cos(pi -pi/4) = cos(3pi/4) = -root(2)/2

 

[cossine]

thank you, but how did you figure that cos 3pie/4 = -root 2/2

You need knowledge of two things
1) related angles and the unit circle
2) special triangle used to find sin/cos/tan of angles 30, 45, 60 degrees

Refer to a textbook or YouTube

 

[Average Boreduser]

thank you, but how did you figure that cos 3pie/4 = -root 2/2

the rt2/2=1/rt2