איך לפשט את (תטה) = sin4theta-cos6theta פונקציות טריגונומטריות של יחידת תטה?

תשובה:

(תטה) ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ theta) -cos (theta) ^ 6 #

הסבר:

נשתמש בשני הזהויות הבאות:

#sin (A + -B) = sinAcosB + -cosAsinB #

#cos (A + -B) = cosAcosB sinAsinB #

# 2 (2thin) (2thein) cos (2theta) = 2 (2sin (theta) cos (theta)) (cos ^ 2 (theta) -Sin ^ 2 (theta)) = 4sin (theta) cos ^ 3 (theta) -4sin ^ 3 (theta) cos (theta) #

#cos (6theta) = cos ^ 2 (3theta) -Sin ^ 2 (3theta) #

# 2 (חטא (2theta) cos (theta) + cos (2theta) חטא (theta)) ^ 2 # (cos (2theta) cos (theta)

# (cos (theta) (cos ^ 2 (theta) - sin ^ 2 (theta)) - 2sin ^ 2 (theta) cos (theta)) ^ 2 (2cos ^ 2 (theta) חטא (theta) + חטא (theta) (cos ^ 2 (theta) -Sin ^ 2 (theta)) ^ 2 #

מס '2 (תטא) - (2) (2) 2 (תטא) חטא (תטא) + cos ^ 2 (theta) חטא (theta) -Sin ^ 3 (theta)) ^ 2 #

# 2 (3 cos ^ 2 (theta) חטא (theta) -Sin ^ 3 (theta)) ^ 2 #

(תטה) 6 (תאטה) - סין ^ 2 (תטה) cos ^ 4 (theta) + 6sin ^ 4 (theta) cos ^ 2 (theta) -Sin ^ 6 (theta) #

# thin (4thethe) -cos (6theta) = 4sin (theta) cos ^ 3 (theta) 4sin ^ 3 (theta) cos (theta) - (cos ^ 6 (theta) 6sin ^ 2 (theta) cos ^ 4 (תטה) + 9 (4) (תטה) cos ^ 2 (theta) -9sin ^ 2 (theta) cos ^ 4 (theta) + 6sin ^ 4 (theta) cos ^ 2 (theta) - 6 ^ (תטה)) #

(תטה) 6 (תטה) + 6sin ^ 2 (theta) cos ^ 4 (theta) -9sin ^ 4 (theta) cta ^ 2 (theta) + 9sin ^ 2 (theta) cos ^ 4 (theta) 6sin ^ 4 (theta) cos ^ 2 (theta) + חטא ^ 6 (theta) #

# תטא (^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ * (theta) -cos (theta) ^ 6 #