Trig Ratios for Any Angle: CAST & Reference Angles (Grade 10)

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Grade 10 · Trigonometry

EXAM-STYLE CLASS TEST

Marks

Duration

50 minutes

Questions

Name:

Class:

Date:

Mark

/ 33

Instructions and Information

Answer ALL the questions in this question paper.
Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
Show ALL calculations clearly.
Show all units where applicable.
Number the answers correctly according to the numbering system used in this question paper.
A non-programmable calculator may be used, unless stated otherwise.
Write neatly and legibly.

Question 1

[10 MARKS]

Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.

1.1
305° lies in …
(1)
A)the first quadrant
B)the second quadrant
C)the fourth quadrant
D)the third quadrant
1.2
The reference angle for 210° is …
(1)
A)60°
B)30°
C)150°
D)210°
1.3
cos 120° = …
(1)
A)−1/2
B)1/2
C)−(√3)/2
D)(√3)/2
1.4
sin θ < 0 and cos θ > 0 in …
(1)
A)the first quadrant
B)the second quadrant
C)the third quadrant
D)the fourth quadrant
1.5
P(−3 ; 4) lies on the terminal arm of θ. Then cos θ = …
(1)
A)4/5
B)−4/3
C)−3/5
D)3/5
1.6
tan 225° = …
(1)
A)−1
B)1
C)√3
D)0
1.7
If sin θ = 12/13 and θ is obtuse, then cos θ = …
(1)
A)−5/13
B)5/13
C)−12/5
D)5/12
1.8
cosec 30° = …
(1)
A)1/2
B)2/(√3)
C)√3
D)2
1.9
sec θ is undefined when θ = …
(1)
A)0°
B)180°
C)90°
D)45°
1.10
sin 330° + cos 240° = …
(1)
A)0
B)−1
C)1
D)−√3

Answer grid — circle your answers for Question 1

1.1	A	B	C	D
1.2	A	B	C	D
1.3	A	B	C	D
1.4	A	B	C	D
1.5	A	B	C	D
1.6	A	B	C	D
1.7	A	B	C	D
1.8	A	B	C	D
1.9	A	B	C	D
1.10	A	B	C	D

Question 2

[10 MARKS]

P(−5 ; 12) lies on the terminal arm of θ, as shown in the diagram below.

2.1
Calculate the length of OP.
(2)
2.2
Write down the values of sin θ, cos θ and tan θ.
(3)
2.3
Determine the value of cosec θ + cot θ.
(3)
2.4
Explain, without using a calculator, why 90° < θ < 180°.
(2)

Question 3

[13 MARKS]

Answer the following WITHOUT using a calculator.

3.1
Evaluate (sin 210° × cos 330°)/(tan 135°).
(5)
3.2
If 13 cos θ + 5 = 0 and 180° < θ < 360°, determine the value of sin θ + tan θ.
(5)
3.3
Explain why cosec 180° is undefined.
(3)

TOTAL: 33 marks

This question paper consists of 3 questions.