Hint
The two angles are acute in these cases. Substitute into the compound-angle formula with the correct signs.
Worked solution
(a)
Substitute into the compound-angle formula with the correct signs.
\(\displaystyle \frac{3}{5}\)
Answer: \(\displaystyle \frac{3}{5}\)
(b)
Substitute into the compound-angle formula with the correct signs.
\(\displaystyle \frac{4}{5}\)
Answer: \(\displaystyle \frac{4}{5}\)
(c)
Substitute into the compound-angle formula with the correct signs.
\(\displaystyle \frac{123}{836}\)
Answer: \(\displaystyle \frac{123}{836}\)
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: Substitute into the compound-angle formula with the correct signs.
- 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: Cosine uses the opposite sign before the sine product.
(b) · 2 marks
- 1 mark: Substitute into the compound-angle formula with the correct signs.
- 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: Do not replace sin(A+B) by sinA+sinB.
(c) · 2 marks
- 1 mark: Substitute into the compound-angle formula with the correct signs.
- 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: Cosine uses the opposite sign before the sine product.
Total: 6 marks.