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Quiz about Maths Topic 4 Trigonometry
Quiz about Maths Topic 4 Trigonometry

Maths Topic 4: Trigonometry Trivia Quiz


This quiz will cover different areas of trigonometry including 2D and 3D problems, trigonometric identies and equations, sine and cosine rules, and different kinds of angle formulae. You will need pen, paper and a calculator for this quiz. Good luck.

A multiple-choice quiz by dialga483. Estimated time: 6 mins.
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Author
dialga483
Time
6 mins
Type
Multiple Choice
Quiz #
365,997
Updated
Dec 03 21
# Qns
20
Difficulty
Tough
Avg Score
12 / 20
Plays
230
-
Question 1 of 20
1. If sinx = 2/7, then what is the exact value of cotx? Hint


Question 2 of 20
2. Which trigonometric ratio is equal to cosec(90-x)? Hint


Question 3 of 20
3. If tanx = 0.486, then what is x in degrees and minutes? Hint


Question 4 of 20
4. Triangle ABC has a hypotenuse equal to 18.2cm, one acute angle equal to 39 degrees, 49 minutes, and the adjacent side to the angle equal to x. What is the value of x, to the nearest whole number? Hint


Question 5 of 20
5. A triangle has an acute angle equal to x, with the opposite side equal to 3.5 and the hypotenuse equal to 8.2. What is the value of x, in degrees and minutes? Hint


Question 6 of 20
6. A boy is flying his kite in the park. If the string of the kite is 20m long, and the angle of elevation is measured to be 47 degrees, how high above the ground is the kite, to 2 decimal places? Hint


Question 7 of 20
7. The bearing of B from X is 130 degrees. What is the bearing of X from B? Hint


Question 8 of 20
8. What is the value of sin^2(60)+cos^2(45)? Hint


Question 9 of 20
9. If sinx = -3/5 and cosx is positive, then what is the value of tanx? Hint


Question 10 of 20
10. For what values of x does 2sin^2(x) = 1? Hint


Question 11 of 20
11. (1-cosx)/sin^2(x) is equal to which other trigonometric expression? Hint


Question 12 of 20
12. Triangle XYZ has angle XYZ equal to 103, angle YXZ equal to 53 and YZ equal to 8cm. What is the length of XZ, to the nearest whole number? Hint


Question 13 of 20
13. Triangle ABC has AB is equal to 5.6 cm, BC is equal to 6.4 cm and angle ABC is equal to 112 degrees, 32 minutes. What is the length of AC, to 2 decimal places? Hint


Question 14 of 20
14. Triangle ABC has AB equal to 4.3, BC equal to 5.8 and angle CBA equal to 106 degrees, 22 minutes. What is the total area of the triangle, to 2 decimal places? Hint


Question 15 of 20
15. The elevation of a hill at a point A due east of it is 39 degrees. At a point B, due south of A, the angle of elevation of the hill is 27 degrees. If the distance from A to B is 500m, what is the height of the hill, to 1 decimal place? Hint


Question 16 of 20
16. What is the exact value of cos75? Hint


Question 17 of 20
17. What is the exact value of 2tan15/(1-tan^2(15))? Hint


Question 18 of 20
18. If t = tan(x/2), then in terms of t, which is the correct expression for cosx? Hint


Question 19 of 20
19. For what values of x does tan(x+60)= -tanx? Hint


Question 20 of 20
20. What is the general solution, in degrees, of the equation tanx = 1? Hint



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Quiz Answer Key and Fun Facts
1. If sinx = 2/7, then what is the exact value of cotx?

Answer: 3sqrt(5)/2

To solve this question, we first need to work out the length of the third side, which can be done through Pythagoras.
So since sinx = 2/7, the opposite side is 2, and the hypotenuse is 7
Therefore,
7^2-2^2=45
Therefore the adjacent side length is sqrt(45), or 3sqrt(5).
Now cotx is adjacent/opposite
So, cotx= 3sqrt(5)/2
2. Which trigonometric ratio is equal to cosec(90-x)?

Answer: secx

To solve this question, we can use a right-angled triangle with acute angles x and 90-x. For the angle 90-x, the adjacent side is equal to b, the opposite side is equal to a, and the hypotenuse is equal to c. Since the cosecant ratio is hypotenuse/opposite, therefore cosec(90-x) is equal to c/a. The secant ratio is hypotenuse/adjacent. Looking at the angle x, secx is equal to c/a.
Therefore, secx = cosec(90-x).
3. If tanx = 0.486, then what is x in degrees and minutes?

Answer: 25 degrees, 55 minutes

This is a question that can be solved on a calculator
So, tanx = 0.486
x = arctan(0.486)
x = 25.9197519
Therefore, x = 25 degrees, 55 minutes.
4. Triangle ABC has a hypotenuse equal to 18.2cm, one acute angle equal to 39 degrees, 49 minutes, and the adjacent side to the angle equal to x. What is the value of x, to the nearest whole number?

Answer: 14 cm

From the information given, we can use the cosine ratio to solve this question.
So,
cos(39d,49m)= x/18.2
x = 18.2cos(39d,49m)
x = 13.97937069
Therefore, x = 14cm, rounded up.
5. A triangle has an acute angle equal to x, with the opposite side equal to 3.5 and the hypotenuse equal to 8.2. What is the value of x, in degrees and minutes?

Answer: 25 degrees, 16 minutes

From the information given, we can use the sine ratio to solve this question.
So,
sinx = 3.5/8.2
x = arcsin(3.5/8.2)
x = 25.26650518
Therefore, x = 25 degrees, 16 minutes.
6. A boy is flying his kite in the park. If the string of the kite is 20m long, and the angle of elevation is measured to be 47 degrees, how high above the ground is the kite, to 2 decimal places?

Answer: 14.63m

Using the information given, we can draw a right-angled triangle, with hypotenuse 20m, an acute angle of 47, and the opposite side of the angle to be x.
So,
sin47 = x/20
x = 20sin47
x = 14.62707403
Therefore, x = 14.63m
7. The bearing of B from X is 130 degrees. What is the bearing of X from B?

Answer: 310 degrees

Bearings are measured starting from a north line in a clockwise direction. From the information given, we can see that point B is south-east of point X. To find the bearing of X from B, we would need to find the reflex angle at B.
Using the north line at B, and co-interior angles,
180 - 130 = 50
Therefore
360 - 50 = 310

Therefore, the bearing of X from B is 310 degrees.
8. What is the value of sin^2(60)+cos^2(45)?

Answer: 1.25

To solve this question, we can use exact values for sin60 and cos45
So, sin60=sqrt(3)/2, cos45=1/sqrt(2)
Therefore,
(sqrt(3)/2)^2+(1/sqrt(2))^2
= 0.75+0.5
= 1.25
9. If sinx = -3/5 and cosx is positive, then what is the value of tanx?

Answer: -3/4

From the information given, we can work out that the remaining side is equal to 4. We can also see that since sinx is negative and cosx is positive, that the answer lies in the 4th quadrant. This makes tanx negative.
Therefore, tanx = -3/4.
10. For what values of x does 2sin^2(x) = 1?

Answer: 45, 135, 225, 315

2sin^2(x)= 1
sin^2(x)= 1/2
sin(x) = +-(1/sqrt(2))
Basic angle = 45
Angle lies in all quadrants
Therefore,
x = 45, 180-45, 180+45, 360-45
x = 45, 135, 225, 315
11. (1-cosx)/sin^2(x) is equal to which other trigonometric expression?

Answer: 1/(1+cosx)

We can use trigonometric identities, to find the correct expression.
So, using sin^2(x)+cos^2(x)= 1
(1-cosx)/sin^2(x)
=(1-cosx)/(1-cos^2(x))
=(1-cosx)/((1-cosx)(1+cosx))
= 1/(1+cosx)
Therefore, (1-cosx)/sin^2(x)= 1/(1+cosx).
12. Triangle XYZ has angle XYZ equal to 103, angle YXZ equal to 53 and YZ equal to 8cm. What is the length of XZ, to the nearest whole number?

Answer: 10cm

To solve this question, we need to use the sine rule,
which is, a/sinA = b/sinB = c/sinC.
So,
XZ/sin103 = 8/sin53
XZ = 8sin103/sin53
XZ = 9.760348019
Therefore, XZ is equal to 10cm.
13. Triangle ABC has AB is equal to 5.6 cm, BC is equal to 6.4 cm and angle ABC is equal to 112 degrees, 32 minutes. What is the length of AC, to 2 decimal places?

Answer: 9.99 cm

To solve this question, we need to use the cosine rule,
which is, a^2=b^2+c^2-2bccosA.
So,
AC^2 = 5.6^2+6.4^2-2(5.6)(6.4)cos(112d,32m)
AC^2 = 99.78927117
AC = 9.989458002
Therefore, AC equals 9.99cm.
14. Triangle ABC has AB equal to 4.3, BC equal to 5.8 and angle CBA equal to 106 degrees, 22 minutes. What is the total area of the triangle, to 2 decimal places?

Answer: 11.96 units^2

We can solve this question by using the formula for area, A=(1/2)absinC.
So,
A =(1/2)(4.3)(5.8)sin(106d,22m)
A = 11.96469156
Therefore, the area of the triangle is 11.96 units^2.
15. The elevation of a hill at a point A due east of it is 39 degrees. At a point B, due south of A, the angle of elevation of the hill is 27 degrees. If the distance from A to B is 500m, what is the height of the hill, to 1 decimal place?

Answer: 160.3 m

If we let the top of the hill be point H, then from the information given, we can see that ABH is a right-angled triangle, with angle HBA equal to 27, and AB equal to 500.
So,
Tan27 = AH/500
AH = 500tan27
Now, if we let the height of the hill equal h
Then, sin39 = h/AH
h = AHsin39
h = 500tan(27)sin(39)
h = 160.3273776
Therefore, the height of the hill is 160.3m.
16. What is the exact value of cos75?

Answer: (sqrt(6)-sqrt(2))/4

To solve this question, we need to use the formula cos(A+B)=cosAcosB-sinAsinB.
So,
cos75
=cos(45+30)
=cos45cos30-sin45sin30
Then using exact values,
=(1/sqrt(2))(sqrt(3)/2)-(1/sqrt(2))(1/2)
= sqrt(3)/2sqrt(2)-1/2sqrt(2)
=(sqrt(3)-1)/2sqrt(2) x sqrt(2)/sqrt(2)
=(sqrt(6)-sqrt(2))/4
17. What is the exact value of 2tan15/(1-tan^2(15))?

Answer: 1/sqrt(3)

To solve this question, we need to use the rule,
Tan(2A)=2TanA/(1-Tan^2(A))
So,
2tan15/(1-tan^2(15))
= tan(2(15))
= tan30
= 1/sqrt(3)
Therefore, the exact value of 2tan15/(1-tan^2(15)) is 1/sqrt(3).
18. If t = tan(x/2), then in terms of t, which is the correct expression for cosx?

Answer: (1-t^2)/(t^2+1)

To solve this question, we first need to make a triangle with x/2 as an acute angle, and t and 1 as the opposite and adjacent sides respectively. Using this, we can work out the hypotenuse to be sqrt(t^2+1).
Therefore,
sin(x/2)= t/sqrt(t^2+1)
cos(x/2)= 1/sqrt(t^2+1)
Now, we can use the rule cos2x = cos^2(x)-sin^2(x)
so, cosx = cos^2(x/2)-sin^2(x/2)
cosx =(1/sqrt(t^2+1))^2-(t/sqrt(t^2+1))^2
cosx = 1/(t^2+1)-t^2/(t^2+1)
Therefore, cosx = (1-t^2)/(t^2+1).
19. For what values of x does tan(x+60)= -tanx?

Answer: 60, 150, 240, 330

To solve this question, we first need to expand the left hand side of the equation.
So,
Tan(x+60)= -tanx
(tanx+tan60)/(1-tan(x)tan(60))= -tanx
(tanx+sqrt(3))/(1-sqrt(3)tan(x))= -tanx
tanx+sqrt(3) = -tanx+sqrt(3)tan^2(x)
sqrt(3)tan^2(x)-2tanx-sqrt(3)= 0
This can then be solved like a quadratic
(sqrt(3)tanx+1)(tanx-sqrt(3))= 0
tanx = -1/sqrt(3), tanx=sqrt(3)
For the first solution,
basic angle = 30
angle lies in 2nd, 4th quadrants
Therefore, x = 180-30, 360-30
x = 150, 330
For the second solution,
basic angle = 60
angle lies in 1st, 3rd quadrants
Therefore, x = 60, 180+60
x = 60, 240
20. What is the general solution, in degrees, of the equation tanx = 1?

Answer: x = 180n+45

The general solution of equation involving tan is x = 180n+a, where a is the basic angle from the given equation. In this case, a = 45, therefore, x = 180n+45.
Source: Author dialga483

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