Moderate -0.8 This is a straightforward trigonometric equation requiring standard algebraic manipulation (collecting like terms to get 4sin²x = 6cos²x, then tan²x = 3/2) followed by routine application of inverse trig and quadrant analysis. The technique is direct with no conceptual obstacles, making it easier than average but not trivial due to the algebraic setup and multiple solutions required.
[tan x = (±)1.225 or sin x = (±)0.7746 or cos x = (±)0.6325]
x= 50.8 (Allow 0.886 (rad))
Another angle correct
x=50.8°, 1 29.2°, 230.8°, 309.2°
Answer
Marks
[ 0.886, 2.25/6, 4.03, 5.40 (rad) ]
M1
A1
A1
Answer
Marks
Guidance
A1
[4]
Or 4 ( 1−cos2x ) =6cos2x
Or any other angle correct
Ft from 1st angle (Allow radians)
All 4 angles correct in degrees
Question 3:
3 | 6
4sin2x=6cos2x⇒tan2x= or 4sin2x=6 ( 1−sin2x )
4
[tan x = (±)1.225 or sin x = (±)0.7746 or cos x = (±)0.6325]
x= 50.8 (Allow 0.886 (rad))
Another angle correct
x=50.8°, 1 29.2°, 230.8°, 309.2°
[ 0.886, 2.25/6, 4.03, 5.40 (rad) ] | M1
A1
A1
A1 | [4] | Or 4 ( 1−cos2x ) =6cos2x
Or any other angle correct
Ft from 1st angle (Allow radians)
All 4 angles correct in degrees
Showing all necessary working, solve the equation $6\sin^2 x - 5\cos^2 x = 2\sin^2 x + \cos^2 x$ for $0° \leq x \leq 360°$. [4]
\hfill \mbox{\textit{CAIE P1 2016 Q3 [4]}}