Hint
Use radians unless degrees are explicitly requested. Raise the positive modulus to the integer power.
Worked solution
(a)
\(r^n=625\)
Answer: \(625\).
Answer: \(625\)
(b)
\(\displaystyle 5^{4}\cos (\frac{4\pi }{6})= - 312.5\)
Answer: \(-312.5\).
Answer: \(\approx -312.5\)
(c)
\(\displaystyle 5^{4}\sin (\frac{4\pi }{6})= 541.265877365274\)
Answer: \(541.265877365274\).
Answer: \(\approx 541.265877365274\)
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.