bjr
a et b sont des angles aigus (sinus, cosinus et tangente positifs)
1)
méthode 1 :
tan a = sin a / cosa
√7/3 = sin a / (3/4)
sin a = (√7/3) x (3/4)
sin a = √7/4
méthode 2 :
sin²a + cos²a = 1
sin²a + (3/4)² = 1
sin²a = 1 - 9/16
sin²a = 16/16 - 9/16
sin²a = 7/16
sin a = √7/4
2)
cos b = 3 sin b
3 sin b = cos b
3 sin b/cos b = 1
3 tan b = 1
tan b = 1/3
sin²b + cos²b = 1
sin²b + (3sin b)² = 1
sin²b + 9 sin²b = 1
10 sin²b = 1
sin²b = 1/10
sin b = 1/√10
sin b = √10/10
cos²b = 1 - sin²b
cos²b = 1 - 1/10
cos²b = 9/10
cos b = 3/√10
cosb = 3√10/10
