A-Level AQA Maths Pure Trigonometric Equations: 5 (a) Sketch the graph of $y =

5 (a) Sketch the graph of $y = ext{sin } 2x$ for $0^{ ext{}} ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } \text{ } ext{ }orall x$ $0^{ ext{}} ext{ } ext{ } ext{ } ext{ } \leq x \leq 360^{ ext{}} ext{ }$ [2 marks] 5 (b) The equation 5 (b) The equation $ ext{sin } 2x = A$ has exactly two solutions for $0^{ ext{}} \leq x \leq 360^{ ext{}}$ State the possible values of $A$ - AQA - A-Level Maths Pure - Question 5 - 2022 - Paper 3

Question 5

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5 (a) Sketch the graph of $y = ext{sin } 2x$ for $0^{ ext{}} ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ ... show full transcript

Worked Solution & Example Answer:5 (a) Sketch the graph of $y = ext{sin } 2x$ for $0^{ ext{}} ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } ext{ } \text{ } ext{ }orall x$ $0^{ ext{}} ext{ } ext{ } ext{ } ext{ } \leq x \leq 360^{ ext{}} ext{ }$ [2 marks] 5 (b) The equation 5 (b) The equation $ ext{sin } 2x = A$ has exactly two solutions for $0^{ ext{}} \leq x \leq 360^{ ext{}}$ State the possible values of $A$ - AQA - A-Level Maths Pure - Question 5 - 2022 - Paper 3

Step 1

Sketch the graph of $y = ext{sin } 2x$ for $0^{ ext{}} \leq x \leq 360^{ ext{}}$

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Answer

The function $y = ext{sin } 2x$ oscillates between -1 and 1.
Since the amplitude of the sine function is 1, there will be peaks at these points:
- At $x = 0^{ ext{}}$ , $y = 0$ .
- At $x = 90^{ ext{}}$ , $y = 1$ .
- At $x = 180^{ ext{}}$ , $y = 0$ .
- At $x = 270^{ ext{}}$ , $y = -1$ .
- At $x = 360^{ ext{}}$ , $y = 0$ .
The graph completes one full period between $0^{ ext{}}$ and $180^{ ext{}}$ , and another between $180^{ ext{}}$ and $360^{ ext{}}$ .
The sketch should reflect these points, showing a smooth wave pattern starting and ending at the origin with two complete oscillations within the defined interval.

Step 2

State the possible values of $A$

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Answer

The equation $ext{sin } 2x = A$ will have two solutions when the value of $A$ lies within the range of the sine function, which oscillates between -1 and 1. Thus, the possible values of $A$ are:

$-1 < A < 1$

Sketch the graph of $y = ext{sin } 2x$ for $0^{ ext{}} \leq x \leq 360^{ ext{}}$

State the possible values of $A$

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