A-LevelMathematicsTrigonometry9709/21 · May/June 2017 · Q57 Marks
Express 2 cos θ + (√5) sin θ in the form Rcos(θ – α) where R > 0 and 0° < α < 90°, giving the value of α correct to 2 decimal places.
- (i)Express 2 cos θ + (√5) sin θ in the form Rcos(θ – α) where R > 0 and 0° < α < 90°, giving the value of α correct to 2 decimal places.[3]
- (ii)Hence solve the equation 2 cos θ + (√5) sin θ = 1 for 0° < θ < 360°.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- [B1] State R = 3
- [M1] Use appropriate trigonometric formula to find α
- [A1] Obtain 48.19 with no errors seen
- [M1] Carry out evaluation of cos⁻¹(1/R) (=70.528...)
- [A1] Obtain correct answer 118.7
- [M1] Carry out correct method to find second answer
- [A1] Obtain 337.7 and no others between 0 and 360
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →