PLC Papers
Created For:
Year 11 Topic Practice Paper: Trigonometric Ratios
Standard trigonometric ratios 1
Objective:
Grade 7
Know and derive the exact values for Sin and Cos 0, 30, 45, 60 and 90 and Tan 0, 30, 45
and 60 degrees.
Question 1.
A right angled triangle has the dimensions as shown in the diagram.
Using the diagram, or otherwise, state the exact values of:
2
√3
(a) Sin 60
(b) Cos 60
1
(c) Tan 60
(d) Sin 30
(e) Cos 30
(f) Tan 30
(Total 6 marks)
Question 2.
Using the triangle shown, or otherwise, find the exact values of:
(a) Sin 45
√2
1
(b) Cos 45
(c) Tan 45
1
(d) Sin 90
(Total 4 marks)
Total /10
PiXL PLC 2017 Certification
Standard trigonometric ratios 2
Objective:
Grade 7
Know and derive the exact values for Sin and Cos 0, 30, 45, 60 and 90 and Tan 0, 30, 45
and 60 degrees.
Question 1.
A right angled triangle has the dimensions as shown in the diagram.
Using the diagram, or otherwise, state the exact values of:
5
y
3
(a) Sin y
x
(b) Cos y
4
(c) Tan y
(d) Sin x
(e) Cos x
(f) Tan x
(Total 6 marks)
Question 2.
State the values of:
(a) Tan 0
(b) Cos 90
(Total 2 marks)
Question 3.
The relationship Sin 30 = Cos 60, can be found for other values of sin and cos. What must the angles
add up to for this relationship to work?
(Total 2 marks)
Total /10
PiXL PLC 2017 Certification
Standard trigonometric ratios 3
Objective:
Grade 7
Know and derive the exact values for Sin and Cos 0, 30, 45, 60 and 90 and Tan 0, 30, 45
and 60 degrees.
Question 1.
Use the triangle to write cosθ in terms of x and hence,
Or otherwise, work out the value of x.
(Total 6 marks)
PiXL PLC 2017 Certification
Question 2.
ABC is a right angled triangle and P is a point on AB.
2
Tan� = .
3
Work out the length of BC
(Total 4 marks)
Total /10
PiXL PLC 2017 Certification
Standard trigonometric ratios 4
Objective:
Grade 7
Know and derive the exact values for Sin and Cos 0, 30, 45, 60 and 90 and Tan 0, 30, 45
and 60 degrees.
Question 1.
Show that angle x is 60 0.
(Total 6 marks)
PiXL PLC 2017 Certification
Question 2.
√3
2
Use the triangle shown to prove that sin60= .
(Total 4 marks)
Total /10
PiXL PLC 2017 Certification
PLC Papers
Created For:
Year 11 Topic Practice Paper: Trigonometric Ratios
Standard trigonometric ratios 1
Objective:
Grade 7
Solutions
Know and derive the exact values for Sin and Cos 0, 30, 45, 60 and 90 and Tan 0, 30, 45
and 60 degrees.
Question 1.
A right angled triangle has the dimensions as shown in the diagram.
Using the diagram, or otherwise, state the exact values of:
(a) Sin 60 =
(b) Cos 60=
(c) Tan 60=
(d) Sin 30=
(e) Cos 30=
(f) Tan 30=
���
=
���
=
���
=
���
=
ℎ��
ℎ��
���
ℎ��
���
=
���
=
ℎ��
���
2
√3
√3
2
1
2
1
√3
1
1
2
√3
2
1
√3
(Total 6 marks)
Question 2.
Using the triangle shown, or otherwise, find the exact values of:
(a) Sin 45=
(b) Cos 45=
(c) Tan 45=
(d) Sin 90=
���
ℎ��
=
1
√2
���
=
���
=1
���
=1
ℎ��
���
ℎ��
√2
1
1
√2
1
(Total 4 marks)
Total /10
PiXL PLC 2017 Certification
Standard trigonometric ratios 2
Objective:
Grade 7
Solutions
Know and derive the exact values for Sin and Cos 0, 30, 45, 60 and 90 and Tan 0, 30, 45
and 60 degrees.
Question 1.
A right angled triangle has the dimensions as shown in the diagram.
Using the diagram, or otherwise, state the exact values of:
(a) Sin y =
���
ℎ��
���
=
���
=0.6
(c) Tan y =
(d) Sin x =
���
ℎ��
(e) Cos x =
(f) Tan x =
4
4
3
���
=0.8
���
= 0.75
ℎ��
���
3
x
=0.6
ℎ��
y
=0.8
���
(b) Cos y =
5
(Total 6 marks)
Question 2.
State the values of:
(a) Tan 0 = 0
(b) Cos 90 = 0
(Total 2 marks)
Question 3.
The relationship Sin 30 = Cos 60, can be found for other values of sin and cos. What must the angles
add up to for this relationship to work?
90
(Total 2 marks)
Total /10
PiXL PLC 2017 Certification
Standard trigonometric ratios 3
Objective:
Grade 7
Solutions
Know and derive the exact values for Sin and Cos 0, 30, 45, 60 and 90 and Tan 0, 30, 45
and 60 degrees.
Question 1.
Use the triangle to write cosθ in terms of x and hence,
Or otherwise, work out the value of x.
From triangle ABD:
Cosθ=
9
M1 for use of adj/hyp
�
A1 for 9/x
From triangle ABC:
Cosθ=
�
16
Equate Fractions:
A1 for x/(9+7)
�
=
9
16 �
M1
16x9=x2 so 144=x2
M1 Cross multiplication
X=12 cm
A1
(Total 6 marks)
PiXL PLC 2017 Certification
Question 2.
ABC is a right angled triangle and P is a point on AB.
2
Tan� = .
3
Work out the length of BC
From the smaller triangle:
2
Tan� = =
3
2
3
=
4
��
4
��
BC= 6cm
M1 for recognising that 4 is opposite
M1 for use of tan=opp/adj
M1 for equating fractions
A1
(Total 4 marks)
Total /10
PiXL PLC 2017 Certification
Standard trigonometric ratios 4
Objective:
Grade 7
Solutions
Know and derive the exact values for Sin and Cos 0, 30, 45, 60 and 90 and Tan 0, 30, 45
and 60 degrees.
Question 1.
Show that angle x is 60 0.
Tanx=
12−5√3
4√3−5
12−5√3
4√3−5
×
M1 for use of adj/opp
4√3+5
4√3+5
48√3+60−60−25√3
48+20√3−20√3−25
23√3
23
√3
1
=
√3
1
= ��� �,
X=600
M1 for attempt to rationalise demoninator
M1 for expansion
M1 for simplification
A1 for conclusion
(Total 6 marks)
PiXL PLC 2017 Certification
Question 2.
√3
2
Use the triangle shown to prove that sin60= .
√22 − 12 = √3
Sin (XYZ) = opp/hyp
Sin 60 =
√3
.
2
M1 - Use Pythagoras Theorem to find YZ
A1 – show YZ = √3 convincingly
M1 – correct ratio
A1 – convincing proof
(Total 4 marks)
Total /10
PiXL PLC 2017 Certification