1
Trig Progress Quiz
Question 1
The angle 𝑥 is obtuse.
Find the value of 𝑥.
Give your answer correct to 1 decimal place.
𝑥 = …………………………
°
Question 2
The diagram shows a triangle ABC.
𝐴𝐵 = (2𝑥 + 1) cm, 𝐴𝐶 = (2𝑥 − 1) cm and 𝐵𝐶 = 2√7 cm.
Angle BAC = 60°
Work out the value of 𝑥.
𝑥 = ...........
(3 marks)
www.drfrost.org - Trig Progress Quiz
2
Question 3
Figure 2 shows a plan view of a semicircular garden 𝐴𝐵𝐶𝐷𝐸𝑂𝐴
The semicircle has
• centre 𝑂
• diameter 𝐴𝑂𝐸
• radius 3 m
The straight line 𝐵𝐷 is parallel to 𝐴𝐸 and angle 𝐵𝑂𝐴 is 0.7 radians.
Find angle 𝐵𝑂𝐷 correct to 4 significant figures.
………………………… radians
Question 4
3
It is given that 𝐵 is acute and that sin𝐵 = 4
Find the exact value of tan𝐵.
tan𝐵 = …………………………
Question 5
Convert these measures in radians to degrees.
𝜋
2𝜋 = . . . . . . . . . . . , 𝜋 = . . . . . . . . . . . , 4 = . . . . . . . . . . .
Question 6
Given that
cos (𝜃−20° ) = cos60°
which one of the following is a possible value for 𝜃?
www.drfrost.org - Trig Progress Quiz
3
40° [ ]
140° [ ]
280° [ ]
320° [ ]
(1 mark)
Question 7
3𝜋
Solve 2cos𝑥 + 1 = 0 for 𝑥, where 𝜋 ≤ 𝑥 < 2 .
5𝜋
Ⓐ6 [ ]
7𝜋
Ⓑ6 [ ]
5𝜋
Ⓒ4 [ ]
4𝜋
Ⓓ3 [ ]
(2 marks)
Question 8
Solve the equation for 𝟎° ≤ 𝛉 ≤ 𝟑𝟔𝟎°
*give your answer to the nearest degree
𝜃 = …………………………
𝜃 = …………………………
www.drfrost.org - Trig Progress Quiz
4
Mark scheme
Question 1
𝑥 =131.8 °
sin 𝑥′
Taking 𝑥′as an acute angle, using the sine rule, 11.4 =
sin (32)
8.1
Multiply both sides by 11.4
11.4 × sin (32)
8.1
−1 11.4 × sin (32)
𝑥′ = sin (
)
8.1
°
sin 𝑥′ =
𝑥′ = 48.2
𝑥 = 180 − 48.2 = 131.8 °
Question 2
𝑥 = 2.5
Question 3
1.742radians
Question 4
3√7
7
opp
➀Recall that sin𝐵 = hyp and construct a right-angled triangle based on the value of sin𝐵
3
sin𝐵 = 4
⇒ opp = 3
⇒ hyp = 4
www.drfrost.org - Trig Progress Quiz
5
➁Use Pythagoras' theorem to work out the missing length.
𝑥2 + 32 = 42
⇒ 𝑥 = √7
opp
➂Recall that tan𝐵 = adj and use the missing length to work out the value of tan𝐵
opp
tan𝐵 = adj
3
= √7
=
3√7
7
Question 5
𝜋
2𝜋 = 360, 𝜋 = 180, 4 = 45
Question 6
320°
Question 7
4𝜋
Ⓓ3
www.drfrost.org - Trig Progress Quiz
6
Question 8
𝜃 =225
𝜃 =315
www.drfrost.org - Trig Progress Quiz