Jawaban:

Grafik Fungsi Trigonometri

Penjelasan dengan langkah-langkah:

Cara mendapatkan nilai maksimum dan minimum adalah dengan membuat tabel fungsi

3. y=cos x -√(3) sin x

tabel terlampir.

Substitusikan nilai x dengan

y=cos 0 - √(3) sin 0

=1-√(3)(0)

=1-0

=1

y=cos (π/2)-√(3) sin (π/2)

=cos (90) -√(3) sin (90)

=0-√(3)(1)

=-√(3)

=-1,73 (minimum)

y=cos (π) - √(3) sin (π)

=cos (180)-√(3) sin(180)

=-1 -√(3)(0)

=-1

y=cos (3π/2)-√(3)sin(3π/2)

=cos (3(180)/2) -√(3)sin (3(180)/2)

=cos (270) - √(3) sin (270)

=0-√(3)(-1)

=√(3)

=1,73 (maksimum)

y=cos (2π) - √(3)sin(2π)

=cos (360) - √(3)sin(360)

=1-√(3)(0)

=1-0

=1

4. y=3 cos x+ 4sin x - 1

Tabel terlampir

subsitusikan nilai x dengan

y=3 cos (0) + 4 sin (0) -1

=3 .1 + 4. 0 - 1

=3+0-1

=3-1

=2

y=3 cos (π/2) + 4 sin (π/2) - 1

=3 cos (90) + 4 sin (90) -1

=3 .0 + 4.1 - 1

=0+4-1

=4-1

=3 ( maksimum )

y=3 cos (π) + 4 sin (π) - 1

=3 cos (180) + 4 sin (180) -1

=3 .-1 + 4 .0 -1

= -3+0-1

= -3-1

= -4

y =3 cos (3π/2) + 4 sin (3π/2) - 1

=3 cos (270) + 4 sin (270) -1

=3.0 + 4.-1- 1

=0-4-1

=-5 ( minimum )

y =3 cos (2π) + 4 sin (2π) - 1

=3 cos (360) + 4 sin (360) -1

=3 . 1 + 4. 0 - 1

= 3 + 0 - 1

= 2

5. y= 5

5 sin x + 12 cos x

Tabel terlampir

Substitusikan nilai x dengan

y= 5

5 sin (0) + 12 cos (0)

= 5

5 (0) + 12 (1)

= 5

0 + 12

= 5

12

y = 5

5 sin (π) +12 cos (π)

= 5

5 sin (180) + 12 cos (180)

= 5

5.0 + 12.-1

= 5

0-12

= 5

-12

y = 5

5 sin (π/2) + 12 cos (π/2)

= 5

5 sin (90) + 12 cos (90)

= 5

5.1 + 12.0

= 5

5 + 0

= 5

5

= 1 ( maksimum )

y = 5

5 sin (3π/2) + 12 cos (3π/2)

= 5

5 sin (270) + 12 cos (270)

= 5

5 .-1 + 12 .0

= 5

-5+0

= 5

-5

= -1 ( minimum )

y = 5

5 sin (2π) + 12 cos (2π)

= 5

5 sin (360) + 12 cos (360)

= 5

5.0 + 12.1

= 5

0+12

= 5

12

Demikian

Semoga membantu dan bermanfaat!