Melakar Fungsi Trigonometri

Aplikasi Graf Fungsi Trigonometri

Melukis Graf Fungsi Trigonometri

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Melukis Graf Fungsi Trigonometri

Fungsi Sinus

Imagine a particle on the unit circle, starting at (1,0) and rotating
counterclockwise around the origin. Every position of the particle
corresponds with an angle, θ, where y = sin θ. As the particle moves
through the four quadrants, we get four pieces of the sin graph:

y sin θ θ sin θ
0 0
90° I II π/2 1
0 90° 180° 270° 360° θ π 0
135° 45° 3π/2 −1
III IV 2π 0
II I

180° 0° x

III IV

225° 315°
270°

Fungsi sinus adalah berkala 2π (360°)

Amplitud sin θ

−3π −2π −π 0 π 2π 3π θ

1 kala
2π

sin θ: Domain: all real numbers, (−∞, ∞)
Range: −1 to 1, inclusive [−1, 1]

Fungsi kosinus

Imagine a particle on the unit circle, starting at (1,0) and rotating
counterclockwise around the origin. Every position of the particle
corresponds with an angle, θ, where x = cos θ. As the particle moves
through the four quadrants, we get four pieces of the cos graph:

y cos θ θ cos θ

90° I
0
135° 45° 0 1
π/2 0
II I π −1
3π/2 0
180° 0° x IV θ 2π 1

90° 180° 270° 360°

III IV II III

225° 315°
270°

Fungsi Kosinus adalah berkala 2π (360°)

−3π −2π −π cos θ 2π θ
0π 3π

1 kala
2π

cos θ: Domain: all real numbers, (−∞, ∞)
Range: −1 to 1, inclusive [−1, 1]

Fungsi Tangen

tanθ = sinθ
cos θ

When cos θ = 0, tan θ is undefined.

This occurs every odd multiple of π/2: { … −π/2, π/2, 3π/2, 5π/2, … }

Table from θ = −π/2 to θ = π/2 .

θ tan θ

tanθ adalah berkala π. −π/2 −∞
−π/4
−1

00

π/4 1

π/2 ∞

Graf Fungsi Tangen: Berkala Vertical asymptotes
where cos θ = 0
tan θ

θ tan θ tanθ = sinθ
−π/2 cos θ
−π/4 −∞
−3π/2 −π/2 0 π/2 3π/2 θ
0 −1
π/4 0
π/2 1

∞

1 kala: π

tan θ: Domain: θ ≠ π/2 + πn; i.e., odd multiple of π/2 .
Range: all real numbers (−∞, ∞)

=

0 π 2π

= 2
2

-2

=

0 π 2π

= +
2
1
0

2

=

0 π 2π

= −
2

=

0 π 2π

= −

2

=

0 π 2π

=

2

=

0 π 2π

= | |

= | + |

Modulus, |cos 2x|: graf dipantulkan pada paksi x

Negatif , - sinx: graf disongsangkan