Sketch the graph of $y = ext{sin} \, x$ for $0^{\circ} < x < 360^{\circ}$ - OCR - GCSE Maths - Question 15 - 2017 - Paper 1
Question 15
Sketch the graph of $y = ext{sin} \, x$ for $0^{\circ} < x < 360^{\circ}$.
Solve the equation $5 \, \text{sin} \, x = -3$.
Give all of the solutions in the ran... show full transcript
Worked Solution & Example Answer:Sketch the graph of $y = ext{sin} \, x$ for $0^{\circ} < x < 360^{\circ}$ - OCR - GCSE Maths - Question 15 - 2017 - Paper 1
Step 1
Sketch the graph of $y = \text{sin} \, x$
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Answer
To sketch the graph of y=sinx:
Identify Key Points: The function sine has key points at
0∘ where y=0
90∘ where y=1 (maximum)
180∘ where y=0
270∘ where y=−1 (minimum)
360∘ where y=0.
Plot Points: On graph paper, plot these five key points on the Cartesian plane.
Draw the Curve: Connect these points smoothly, remembering the periodic nature of the sine function. Ensure that the graph reaches a maximum at 90∘ and a minimum at 270∘. The graph should oscillate between 1 and −1, crossing the x-axis at 0∘, 180∘, and 360∘.
Step 2
Solve the equation $5 \text{sin} \, x = -3$
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Answer
To solve for x in the equation 5sinx=−3:
Isolate extsinx:
sinx=5−3​=−0.6
Find Reference Angle: Calculate the reference angle:
θ=arcsin(−0.6)≈−36.87∘
However, since we want angles within 0∘ to 360∘, we can use the reference angle in the relevant quadrants:
Quadrant III: 180∘+36.87∘≈216.87∘
Quadrant IV: 360∘−36.87∘≈323.13∘
Solution: Hence, the solutions in the desired range are:
x≈217∘ or x≈323∘.
