1.
sin (2x + 8°) − cos (2x + 8°) = 0
sin (2x + 8°) = cos (2x + 8°)
tan (2x + 8°) = 1 . . . deel met / divide by cos (2x + 8°)
Skerphoek / Acute angle = 45° (kw. / quad. 1 ; 3)
2x + 8° = 45° + k . 360°
OF / OR
2x + 8° = 180° + 45° + k . 360° ; k ∈ Z
2x = 37° + k . 360° ; k ∈ Z
2x = 217° + k . 360° ; k ∈ Z
x = 18,50° + k . 180° ; k ∈ Z
x = 108,50° + k . 180° ; k ∈ Z
2.
sin (3x − 17°) + cos (3x − 17°) = 0
sin (3x − 17°) = − cos (3x − 17°)
tan (3x − 17°) = − 1 . . . deel met / divide by cos
Skerphoek / Acute angle = 45° (kw. / quad. 2 ; 4)
3x − 17° = 180° − 45° + k . 360°
OF / OR
3x − 17° = 360° − 45° + k . 360° ; k ∈ Z
3x − 17° = 135° + k . 360° ; k ∈ Z
3x − 17° = 315° + k . 360° ; k ∈ Z
3x = 152° + k . 360° ; k ∈ Z
3x = 332° + k . 360° ; k ∈ Z
x = 50,67° + k . 120° ; k ∈ Z
x = 110,67° + k . 120° ; k ∈ Z
3.
4 sin (4x − 18°) − 3 cos (4x − 18°) = 0
4 sin (4x − 18°) = 3 cos (4x − 18°)
tan (4x − 18°) = 0,75 . . . deel met / divide by cos
Skerphoek / Acute angle = 36,869897...° (kw. / quad. 1 ; 3)
4x − 18° = 36,869897...° + k . 360°
OF / OR
4x − 18° = 180° + 36,869897...° + k . 360° ; k ∈ Z
4x − 18° = 36,869897...° + k . 360° ; k ∈ Z
4x − 18° = 180° + 36,869897...° + k . 360° ; k ∈ Z
4x = 54,869897...° + k . 360° ; k ∈ Z
4x = 234,869897...° + k . 360° ; k ∈ Z
x = 13,72° + k . 90° ; k ∈ Z
x = 58,72° + k . 90° ; k ∈ Z
4.
5 sin (6x − 68°) − 4 cos (6x − 68°) = 0
5 sin (6x − 68°) = 4 cos (6x − 68°)
4
tan (6x − 68°) = ─── . . . deel met / divide by cos
5
Skerphoek / Acute angle = 38,6598...° (kw. / quad. 1 ; 3)
6x − 68° = 38,6598...° + k . 360°
OF / OR
6x − 68° = 180° + 38,6598...° + k . 360° ; k ∈ Z
6x − 68° = 38,6598...° + k . 360° ; k ∈ Z
6x − 68° = 180° + 38,6598...° + k . 360° ; k ∈ Z
6x = 106,6598...° + k . 360° ; k ∈ Z
6x = 286,6598...° + k . 360° ; k ∈ Z
x = 17,78° + k . 60° ; k ∈ Z
x = 47,78° + k . 60° ; k ∈ Z
5.
3 sin α + 2 cos α = 0
3 sin α = − 2 cos α
2
tan α = − ─── . . . deel met / divide by cos
3
Skerphoek / Acute angle = 33,69° (kw. / quad. 2 ; 4)
α = 180° − 33,69° + k . 360° ; k ∈ Z
OF / OR
α = 360° − 33,69° + k . 360° ; k ∈ Z
= 146,31° + k . 360° ; k ∈ Z
= 326,31° + k . 360° ; k ∈ Z
6.
2 sin x − cos x = 0
2 sin x = cos x
tan x = 0,5 . . . deel met / divide by cos
Skerphoek / Acute angle = 26,5650...° (kw. / quad. 1 ; 3)
x = 26,5650...° + k . 360° ; k ∈ Z
OF / OR
x = 180° + 26,5650...° + k . 360° ; k ∈ Z
= 26,57° + k . 360° ; k ∈ Z
= 206,57° + k . 360° ; k ∈ Z