GRADE 11_Calculations in four quadrants

CAMI Mathematics:: Grade 11
GRADE 11_Trigonometry
11.9 Calculations in the four quadrants
All the calculations must be accompanied by a diagram.
1.
If -5sin θ = 3 and θ ∈ (270°;360°) , determine cos θ .
2.
If tan α - 4 = 0 and 0° ≤ α ≤ 90°, determine cos α .
3.
If 5tan β = 12 and β ∈ (180°;270°) , determine sin β .
4.
If 5 cos θ = 4 and θ ∈ (0°;90°) , determine tan θ .
5.
If -13cos α = 5 and α ∈ [180°;270°] , determine sin α .
CAMI Mathematics:: Grade 11
MEMO
Calculations in four quadrants
quadrants [7.6.5.1
[7.6.5.1]
7.6.5.1]
1.
-5sin θ = 3
−3 y
sin θ =
=
5
r
2
2
2
r =x +y
5 2 = x 2 + (−3) 2
25 = x 2 + 9
16 = x 2
∴ x = ±4
4 th : x = 4
∴ cos θ =
2.
x 4
=
r 5
tan α - 4 = 0
tan α = 4 =
4 y
=
1 x
r 2 = x2 + y2
r 2 = 12 + 4 2
r 2 = 17
∴ r = 17
∴ cos α =
3.
x
1
=
r
17
5tan β = 12
− 12 y
tan β =
=
−5 x
CAMI Mathematics:: Grade 11
r 2 = x2 + y2
r 2 = (−5) 2 + (−12) 2
r 2 = 169
∴ r = 13
y − 12
=
r
13
∴ sin β =
4.
5 cos θ = 4
4 x
cos θ = =
5 r
r 2 = x2 + y2
52 = 4 2 + y 2
25 = 16 + y 2
9 = y2
∴ y = ±3
1st : y = 3
∴ tan θ =
5.
y 3
=
x 4
-13cos α = 5
−5 x
cos α =
=
13 r
r 2 = x2 + y2
13 2 = (−5) 2 + y 2
169 = 25 + y 2
144 = y 2
∴ y = ±12
3 rd : y = −12
∴ sin α =
y − 12
=
r
13