2023 AISS AM S3 EOY Q5
2023 AISS AM S3 EOY Q5
7 marks
Others>EOY
- Write down the principal value of \({\sin^{-1}\left(-\frac{1}{2}\right)}\) in radians as a multiple of \({\pi}\).[1]
The diagram shows the curve \({y = a\sin{bx} + c}\) for \({0 \leq x \leq \pi}\) radians.The curve has a maximum point at \({\left(\frac{\pi}{4}, 3\right)}\) and a minimum point at \({\left(\frac{3\pi}{4}, -7\right)}\).- Explain why \({c = -2}\).[2]
- Explain why \({b = 2}\).[2]
- Hence find the equation of the curve.[2]
Video Solution:
Video solution locked
A free account saves your progress; this video needs a course plan.
Solution:
Solution locked
680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs a course plan.
Create a free account to practise similar questions.
Answer:(a) \(-\frac{\pi }{6}\)
(b)(i) Since min y = -7 \text{ and } max y =3, centreline y = c at \(y=\frac{3+\left( -7 \right)}{2}=-2\). Therefore \(c=-2\). (ii) Period of \(y=a\sin bx+c\)graph = \(\frac{2\pi }{b}=\pi \) from graph. Therefore, b = 2.
(iii) \(y=5\sin 2x-2\)
Need help? Join our A-Maths tuition classes.
Learn more