Hint
The stated quadrant fixes the signs. Apply the relevant reciprocal or double-angle identity on its domain.
Worked solution
(a)
Apply the relevant reciprocal or double-angle identity on its domain.
\(\displaystyle \frac{89}{64}\)
Answer: \(\displaystyle \frac{89}{64}\)
(b)
Apply the relevant reciprocal or double-angle identity on its domain.
\(\displaystyle \frac{89}{25}\)
Answer: \(\displaystyle \frac{89}{25}\)
(c)
Apply the relevant reciprocal or double-angle identity on its domain.
\(\displaystyle \frac{8}{5}\)
Answer: \(\displaystyle \frac{8}{5}\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternatives and consequential reasoning; an unexplained final answer does not earn a method mark.
(a) · 2 marks
- 1 mark: Apply the relevant reciprocal or double-angle identity on its domain.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: secθ is not \(\displaystyle \frac{1}{\sin\theta}\).
(b) · 2 marks
- 1 mark: Apply the relevant reciprocal or double-angle identity on its domain.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: A squared identity does not by itself determine an unsquared sign.
(c) · 2 marks
- 1 mark: Apply the relevant reciprocal or double-angle identity on its domain.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: secθ is not \(\displaystyle \frac{1}{\sin\theta}\).
Total: 6 marks.