Hint
The quadrant is specified. Use the reference triangle and quadrant sign.
Worked solution
(a)
Use the reference triangle and quadrant sign.
\(\displaystyle - \frac{12}{37}\)
Answer: \(\displaystyle - \frac{12}{37}\)
(b)
Cosine is negative in the stated quadrant.
\(\displaystyle - \frac{35}{37}\)
Answer: \(\displaystyle - \frac{35}{37}\)
(c)
Divide the signed sine by the signed cosine.
\(\displaystyle \frac{12}{35}\)
Answer: \(\displaystyle \frac{12}{35}\)
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: Use the reference triangle and quadrant sign.
- 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 square root alone does not determine the sign of a ratio.
(b) · 2 marks
- 1 mark: Cosine is negative in the stated quadrant.
- 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: Tangent signs are determined by both sine and cosine.
(c) · 2 marks
- 1 mark: Divide the signed sine by the signed cosine.
- 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 square root alone does not determine the sign of a ratio.
Total: 6 marks.