6.4

Trigonometric graphs

9 flashcards to master Trigonometric graphs

Smart Spaced Repetition

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Key Concept Flip

Sketch the graph of y = sin(x) for 0° ≤ x ≤ 360°. Label key points.

Answer Flip

The sine graph starts at (0,0), reaches a maximum of 1 at 90°, returns to 0 at 180°, reaches a minimum of -1 at 270°, and returns to 0 at 360°. Remember its 'wave' shape.

Key Concept Flip

Sketch the graph of y = cos(x) for 0° ≤ x ≤ 360°. Label key points.

Answer Flip

The cosine graph starts at (0,1), reaches 0 at 90°, reaches a minimum of -1 at 180°, returns to 0 at 270°, and ends at 1 at 360°. Think of it as a sine graph shifted left by 90 degrees.

Key Concept Flip

What is the period of the graph y = sin(3x)?

Answer Flip

The period is the length of one complete cycle. For y = sin(bx), the period is 360°/b. Therefore, the period of y = sin(3x) is 360°/3 = 120°.

Definition Flip

What is the amplitude of the graph y = 4cos(x)?

Answer Flip

Amplitude is the maximum displacement from the x-axis. For y = a*cos(x), the amplitude is |a|. Thus, the amplitude of y = 4cos(x) is 4.

Definition Flip

Describe the transformation of y = sin(x) to y = sin(x) + 2.

Answer Flip

The graph of y = sin(x) + 2 is a vertical translation of the graph y = sin(x) by 2 units upwards. All points on the graph are shifted up by 2.

Definition Flip

Describe the transformation of y = cos(x) to y = cos(x - 30°).

Answer Flip

The graph of y = cos(x - 30°) is a horizontal translation of the graph y = cos(x) by 30° to the right. The entire graph is shifted right by 30 degrees.

Key Concept Flip

Sketch the graph of y = tan(x) for -90° < x < 90°. Show any asymptotes.

Answer Flip

The tangent graph starts near -∞ at -90°, passes through (0,0), and approaches +∞ as x approaches 90°. It has vertical asymptotes at x = -90° and x = 90°.

Definition Flip

What is the period of the graph y = tan(x)?

Answer Flip

The period of the tangent function, y = tan(x), is 180°. The graph repeats every 180 degrees.

Key Concept Flip

The graph of y = cos(x) is stretched vertically by a factor of 2. Write the equation of the new graph.

Answer Flip

A vertical stretch by a factor of 2 means multiplying the entire function by 2. The equation of the new graph is y = 2cos(x).

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6.3 3D trigonometry 7.1 Transformations

Key Questions: Trigonometric graphs

What is the amplitude of the graph y = 4cos(x)?

Amplitude is the maximum displacement from the x-axis. For y = a*cos(x), the amplitude is |a|. Thus, the amplitude of y = 4cos(x) is 4.

Describe the transformation of y = sin(x) to y = sin(x) + 2.

The graph of y = sin(x) + 2 is a vertical translation of the graph y = sin(x) by 2 units upwards. All points on the graph are shifted up by 2.

Describe the transformation of y = cos(x) to y = cos(x - 30°).

The graph of y = cos(x - 30°) is a horizontal translation of the graph y = cos(x) by 30° to the right. The entire graph is shifted right by 30 degrees.

What is the period of the graph y = tan(x)?

The period of the tangent function, y = tan(x), is 180°. The graph repeats every 180 degrees.

About Trigonometric graphs (6.4)

These 9 flashcards cover everything you need to know about Trigonometric graphs for your Cambridge IGCSE Mathematics (0580) exam. Each card is designed based on the official syllabus requirements.

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