Question 1: [1 mark]
Choose the correct sketch of the graph y = \text{sin}(x) for the region -360 \degree \leq x \leq 360 \degree.
Answer type: Multiple choice type 1
A: A
B: B
C: C
D: D
ANSWER: B: B
Question 2: [1 mark]
Choose the correct sketch of the graph y = \text{cos}(x) for the region -360 \degree \leq x \leq 360 \degree.
Answer type: Multiple choice type 1
A: A
B: B
C: C
D: D
ANSWER: A: A
Question 3: [1 mark]
Choose the correct sketch of the graph y = \text{tan}(x) for the region -360 \degree \leq x \leq 360 \degree.
Answer type: Multiple choice type 1
A: A
B: B
C: C
D: D
ANSWER: D: D
Question 4:
The graph of y = \text{cos}(x) for -180 \leq x \leq 180 has been drawn on the axes below.
Using the graph, find the solutions to the following equations.
Question 4(a): [1 mark]
\text{cos}(x) = 0
Answer type: Multiple choice type 1
A: x = -90 or x = 90
B: x = -45 or x = 45
C: x = -60 or x = 60
D: x = -180 or x = 180
ANSWER: A: x = -90 or x = 90
WORKING:
Points on the x-axis where y=0.
Question 4(b): [1 mark]
\text{cos}(x) = \dfrac{1}{2}
Multiple choice type 1
A: x = -90 or x = 90
B: x = -45 or x = 45
C: x = -60 or x = 60
D: x = -180 or x = 180
ANSWER: C: x = -60 or x = 60
WORKING:
Points on the x-axis where y=\dfrac{1}{2}.
Question 4(c): [1 mark]
Choose the correct statement to why there are no solutions to the equation \text{cos}(x) = 2.
Answer type: Multiple choice type 2
A: The \text{cos} function only has a range of 1.
B: The \text{cos} function only has a range of 0.
C: (\text{cos}(x))^2 = 0.
D: \dfrac{1}{2} \text{cos}(x) = 0.
ANSWER: A: The \text{cos} function only has a range of 1.
Question 5:
For the following graphs, choose the correct function corresponding to the graph shown.
Question 5(a): [1 mark]
Answer type: Multiple choice type 1
A: Cosine
B: Tangent
C: Sine
D: None of the above
ANSWER: C: Sine
Question 5(b): [1 mark]
Answer type: Multiple choice type 1
A: Cosine
B: Tangent
C: Sine
D: None of the above
ANSWER: A: Cosine
Question 5(c): [1 mark]
Answer type: Multiple choice type 1
A: Cosine
B: Tangent
C: Sine
D: None of the above
ANSWER: B: Tangent
Question 5(d): [1 mark]
Answer type: Multiple choice type 1
A: Cosine
B: Tangent
C: Sine
D: None of the above
ANSWER: D: None of the above
Question 5(e): [1 mark]
Answer type: Multiple choice type 1
A: Cosine
B: Tangent
C: Sine
D: None of the above
ANSWER: C: Sine
Question 5(f): [1 mark]
Answer type: Multiple choice type 1
A: Cosine
B: Tangent
C: Sine
D: None of the above
ANSWER: D: None of the above
Question 6: [2 marks]
The plot of y = \text{sin}(x) between -180 \degree \leq x \leq 180 \degree is seen below as a solid line.
What is the equation of the line represented by a dotted line?
Answer type: Multiple choice type 1
A: y = 2 \text{sin}(x)
B: y = - \text{sin}(x)
C: y = \dfrac{1}{2} \text{sin}(x)
D: y = \text{sin}(2x)
ANSWER: A: y = 2 \text{sin}(x)
Question 7: [2 marks]
Using the following graph, what are the solutions to the equation \text{sin}(x) = \text{cos}(x)?
Answer type: Multiple choice type 1
A: x = -135 or x = 45
B: x = 135 or x = -45
C: x = -90 or x = 90
D: x = -180 or x = 0
ANSWER: A: x = -135 or x = 45
WORKING
x values where the graphs cross.