Hint
Use radians unless degrees are explicitly requested. Raise the positive modulus to the integer power.
Worked solution
(a)
\(r^n=64\)
Answer: \(64\).
Answer: \(64\)
(b)
\(\displaystyle 4^{3}\cos (\frac{3\pi }{5})= - 19.7770876399966\)
Answer: \(-19.7770876399966\).
Answer: \(\approx -19.7770876399966\)
(c)
\(\displaystyle 4^{3}\sin (\frac{3\pi }{5})= 60.8676170428898\)
Answer: \(60.8676170428898\).
Answer: \(\approx 60.8676170428898\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit valid alternative reasoning and consequential working; do not award a reasoning mark for an unexplained final answer.
(a) · 2 marks
- 1 mark: Raise the positive modulus to the integer power.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: Raise the modulus to the power as well as multiplying the angle.
(b) · 2 marks
- 1 mark: Multiply the argument by n before taking cosine.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: Do not confuse an argument with the imaginary part.
(c) · 2 marks
- 1 mark: Multiply the argument by n before taking sine.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: Raise the modulus to the power as well as multiplying the angle.
Total: 6 marks.