mendokusai
Nomor 1 a. cos 4/3 π = cos 240° = cos (180° + 60°) = - cos 60° = -1/2 b. sin 5/6 π = sin 150° = sin (180° - 30°) = sin 30° = 1/2 c. tan 7/4 π = tan 315° = tan (360° - 45°) = - tan 45° = - 1 d. sin - 7/6 π = - sin 7/6 π = - sin 210° = - sin (180° + 30°) = sin 30° = 1/2
nomor 2 a. sin 135° - cos 225° + tan 240° = sin (180° - 45°) - cos (180° + 45°) + tan (180° + 60°) = sin 45° + cos 45° + tan 60° = 1/2 √2 + 1/2 √2 + √3 = √2 + √3 b. 3 tan 5/6 π + 4 cos 11/6 π - sin 2/3 π = 3 tan 150° + 4 cos 330° - sin 120° = 3 tan (180° - 30°) + 4 cos (360° - 30°) - sin (180° - 60°) = - 3 tan 30° + 4 cos 30° - sin 60° = - 3 1/3 √3 + 4 1/2 √3 - 1/2 √3 = -√3 + 2√3 - 1/2 √3 = 1/2 √3 c. sin 90° + cos 240° - sin 330° / sin 180° cos 150° - cos 300° = sin 90° + cos (180° + 60°) - sin (360° - 30°) / sin 180° cos (180° - 30°) - cos (360°- 60°) = sin 90° - cos 60° + sin 30° / sin 180° (- cos 30°) - cos 60° = 1 - 1/2 + 1/2 / 0 (-1/2 √3) - 1/2 = 1 / -1/2 = -2
2 votes Thanks 2
ekamiaww
1a) cos 4/3π = cos 4/3 (180°) = cos 240° = cos (180° + 60°) = - cos 60° = - 1/2 b) sin 5/6π = sin 5/6 (180°) = sin 150° = sin (180° - 30°) = sin 30° = 1/2 c) tan 7/4π = tan 7/4 (180°) = tan 315° = tan (360° - 45°) = - tan 45° = -1 d) sin (-7/6π) = - sin 7/6π = - sin 7/6 (180°) = - sin 210° = - sin (180° + 30°) = - ( - sin 30°) = sin 30° = 1/2
2a) sin 135° - cos 225° + tan 240° = 1/2 √2 - (- 1/2 √2) + √3 = 1/2 √2 + 1/2 √2 + √3 = √2 + √3 b) 3 tan 5/6π + 4 cos 11/6π - sin 2/3π = 3 tan 150° + 4 cos 330° - sin 120° = 3 (- 1/3 √3) + 4 (1/2 √3) - (1/2 √3) = - √3 + 2√3 - 1/2 √3 = 1/2 √3 c) sin 90° + cos 240° - sin 330° sin 180° x cos 150° - cos 300° = 1 + (-1/2) - (-1/2) 0 x 1/2 √3 - 1/2 = 1 - 1/2 + 1/2 0 - 1/2 = 1 -1/2 = 1 x - 2/1 = -2
a. cos 4/3 π = cos 240° = cos (180° + 60°) = - cos 60° = -1/2
b. sin 5/6 π = sin 150° = sin (180° - 30°) = sin 30° = 1/2
c. tan 7/4 π = tan 315° = tan (360° - 45°) = - tan 45° = - 1
d. sin - 7/6 π = - sin 7/6 π = - sin 210° = - sin (180° + 30°) = sin 30° = 1/2
nomor 2
a. sin 135° - cos 225° + tan 240°
= sin (180° - 45°) - cos (180° + 45°) + tan (180° + 60°)
= sin 45° + cos 45° + tan 60°
= 1/2 √2 + 1/2 √2 + √3
= √2 + √3
b. 3 tan 5/6 π + 4 cos 11/6 π - sin 2/3 π
= 3 tan 150° + 4 cos 330° - sin 120°
= 3 tan (180° - 30°) + 4 cos (360° - 30°) - sin (180° - 60°)
= - 3 tan 30° + 4 cos 30° - sin 60°
= - 3 1/3 √3 + 4 1/2 √3 - 1/2 √3
= -√3 + 2√3 - 1/2 √3
= 1/2 √3
c. sin 90° + cos 240° - sin 330° / sin 180° cos 150° - cos 300°
= sin 90° + cos (180° + 60°) - sin (360° - 30°) / sin 180° cos (180° - 30°) - cos (360°- 60°)
= sin 90° - cos 60° + sin 30° / sin 180° (- cos 30°) - cos 60°
= 1 - 1/2 + 1/2 / 0 (-1/2 √3) - 1/2
= 1 / -1/2
= -2
= cos 240°
= cos (180° + 60°)
= - cos 60°
= - 1/2
b) sin 5/6π = sin 5/6 (180°)
= sin 150°
= sin (180° - 30°)
= sin 30°
= 1/2
c) tan 7/4π = tan 7/4 (180°)
= tan 315°
= tan (360° - 45°)
= - tan 45°
= -1
d) sin (-7/6π) = - sin 7/6π
= - sin 7/6 (180°)
= - sin 210°
= - sin (180° + 30°)
= - ( - sin 30°)
= sin 30°
= 1/2
2a) sin 135° - cos 225° + tan 240° = 1/2 √2 - (- 1/2 √2) + √3
= 1/2 √2 + 1/2 √2 + √3
= √2 + √3
b) 3 tan 5/6π + 4 cos 11/6π - sin 2/3π
= 3 tan 150° + 4 cos 330° - sin 120°
= 3 (- 1/3 √3) + 4 (1/2 √3) - (1/2 √3)
= - √3 + 2√3 - 1/2 √3
= 1/2 √3
c) sin 90° + cos 240° - sin 330°
sin 180° x cos 150° - cos 300°
= 1 + (-1/2) - (-1/2)
0 x 1/2 √3 - 1/2
= 1 - 1/2 + 1/2
0 - 1/2
= 1
-1/2
= 1 x - 2/1
= -2
semoga membantu ya :)