1.
2
tan x =
1
3
tan x =
(M1)
1
(M1)
3
x = 30 or x = 150
(A1)(A1)(C2)(C2)
[4]
2.
(a)
30
Acute angle 30
(M1)
Note: Award the (M1) for 30 and/or quadrant diagram/graph seen.
2nd quadrant since sine positive and cosine negative
= 150
(b)
1
2
tan 150 = ta
1.
(a)
evidence of using area of a triangle
(M1)
1
eg A 2 2 sin
2
A = 2 sin
(b)
A1
N2
METHOD 1
POA =
1
2 2 sin (= 2 sin ( )
2
since sin ( ) = sin
then both triangles have the same area
area OPA =
(A1)
A1
R1
AG
N0
R3
AG
N0
METHOD 2
triangle OPA has the
1.
The following diagram shows a semicircle centre O, diameter [AB], with radius 2.
Let P be a point on the circumference, with POB = radians.
(a)
Find the area of the triangle OPB, in terms of .
(2)
(b)
Explain why the area of triangle OPA is the same as