Trigonometry Practice Questions with Solutions
1.
For each of the following triangles, write down sin A, cos A and tan A.
Give your answers in simplest form.
(i)
Label the sides of the triangle:
(Opp)
(Adj)
(Hyp)
1.
For each of the following triangles, write down sin A, cos A and tan A.
Give your answers in simplest form.
(ii)
Label the sides of the triangle:
(Opp)
(Adj)
(Hyp)
1.
For each of the following triangles, write down sin A, cos A and tan A.
Give your answers in simplest form.
(iii)
Label the sides of the triangle:
(Opp)
(Adj)
(Hyp)
1.
For each of the following triangles, write down sin A, cos A and tan A.
Give your answers in simplest form.
(iv)
Label the sides of the triangle:
(Opp)
(Adj)
(Hyp)
1.
For each of the following triangles, write down sin A, cos A and tan A.
Give your answers in simplest form.
(v)
Label the sides of the triangle:
(Opp)
(Adj)
(Hyp)
1.
For each of the following triangles, write down sin A, cos A and tan A.
Give your answers in simplest form.
(vi)
Label the sides of the triangle:
(Opp)
(Adj)
(Hyp)
2.
Find the measure of the missing side, in the triangle shown.
Hence write down sin A, cos A and tan A. Give your answers in simplest form.
O
2
+ A
2
= H
2
O
2
+ (5·5)
2
= (7·3)
2
O
2
+ 30·25 = 53·29
O
2
= 23·04
O = 4·8
Label the sides of the triangle:
(Opp)
(Adj)
(Hyp)
2.
Find the measure of the missing side, in the triangle shown.
Hence write down sin A, cos A and tan A. Give your answers in simplest form.
(Opp)
(Adj)
(Hyp)
4·8
3.
(i)
Use your calculator to find the value of tan
45˚
.
tan 45° = 1
3.
(ii)
Hence find |
PQ
|
Label the sides of the triangle:
(Opp)
(Adj)
(Hyp)
3.
(iii)
Hence find |
PR
| Give your answer in surd form.
|
PR
|
2
= 7
2
+ 7
2
|
PR
|
2
= 49 + 49
|
PR
|
2
= 98
4.
The diagram shows a right-angled triangle
ABC
.
(i)
|
BC
|
2
+ 4
2
= 5
2
|
BC
|
2
+ 16 = 25
|
BC
|
2
= 25 – 16
|
BC
|
2
= 9
Find |
BC
|
4.
The diagram shows a right-angled triangle
ABC
.
(ii)
Write down sin
BAC
, cos
BAC
and tan
BAC
Label the sides of the triangle:
(Opp)
(Adj)
(Hyp)
4.
The diagram shows a right-angled triangle
ABC
.
(iii)
Show that
5.
A
is an angle, such that
Without finding the angle
A
, find sin
A
and tan
A
.
Step 1:
Find opposite side to angle A
3
2
+ (opp)
2
= 5
2
9 + (opp)
2
= 25
(opp)
2
= 25 – 9
(opp)
2
= 16
(opp) = 4
5.
A
is an angle, such that
Without finding the angle
A
, find sin
A
and tan
A
.
Step 2:
4
6.
B
is an angle, such that sin
Without finding the angle
B
, find cos
B
and tan
B
.
12
2
+
x
2
= 37
2
144 +
x
2
= 1369
x
2
= 1369 – 144
x
2
= 1225
x
= 35
7.
θ
is an angle, such that
(i)
Without finding the angle
θ
, find sin
θ
and cos
θ
H
= 2
7.
θ
is an angle, such that
(ii)
Show that sin
2
A
+ cos
2
A
= 1
sin
2
A
+ cos
2
A
= (sin
A
)
2
+ (cos
A
)
2
sin
2
A
+ cos
2
A
= 1
8.
Use the information given in the diagram to show that sin
+ cos
> tan
sin
+ cos
tan
sin
+ cos
Label the sides of
the triangle:
(Opp)
(Adj)
(Hyp)
9.
The diagram shows two right angled triangles.
Find each of the following. Where appropriate, leave your answer in surd form.
|
SR
|
|
SR
|
2
= 3
2
+ 6
2
= 9 + 36
= 45
(i)
3
9.
The diagram shows two right angled triangles.
Find each of the following. Where appropriate, leave your answer in surd form.
|
PQ
|
|
PQ
|
2
+ 3
2
= 5
2
|
PQ
|
2
+ 9 = 25
|
PQ
|
2
= 25 – 9
(ii)
|
PQ
|
2
= 16
=
4
9.
The diagram shows two right angled triangles.
Find each of the following. Where appropriate, leave your answer in surd form.
(iii)
sin
SRQ
Label the sides of
the triangle
(Opp)
(Adj)
(Hyp)
4
9.
The diagram shows two right angled triangles.
Find each of the following. Where appropriate, leave your answer in surd form.
(iv)
tan
SPQ
Label the sides of
the triangle
(Opp)
(Adj)
(Hyp)
4
9.
The diagram shows two right angled triangles.
Find each of the following. Where appropriate, leave your answer in surd form.
(v)
cos
RSQ
Label the sides of
the triangle
(Opp)
(Adj)
(Hyp)
4
9.
The diagram shows two right angled triangles.
Find each of the following. Where appropriate, leave your answer in surd form.
(vi)
Investigate if
∆SPR
is
right angled.
Therefore, ∆
SPR
is not
right-angled
.
4
Note to Teacher: Use this slide in Slideshow View to display the animated sequences.
Practice questions involving trigonometric ratios sin, cos, and tan for different triangles are provided along with their solutions. The questions cover a variety of scenarios where students are required to determine the trigonometric ratios for given sides in the triangles.
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Presentation Transcript
CHAPTER 20 Trigonometry I Solutions: Practice Questions 2
20 Practice Questions 2 1. For each of the following triangles, write down sin A, cos A and tan A. Give your answers in simplest form. Label the sides of the triangle: (i) Opp Hyp 5 A = = sin (Hyp) 13 (Opp) Adj Hyp 12 13 A = = cos Opp Adj 5 (Adj) A = = tan 12
20 Practice Questions 2 1. For each of the following triangles, write down sin A, cos A and tan A. Give your answers in simplest form. Label the sides of the triangle: (ii) Opp Hyp 8 A = = sin (Hyp) 17 Adj Hyp 15 17 A = = cos (Opp) Opp Adj 8 A = = tan (Adj) 15
20 Practice Questions 2 1. For each of the following triangles, write down sin A, cos A and tan A. Give your answers in simplest form. Label the sides of the triangle: (iii) Opp Hyp 6 60 61 A = = = sin 6 1 A (Hyp) 6 1 1 1 Adj Hyp 1 1 6 1 11 61 = = = cos A (Adj) (Opp) 6 Opp Adj 6 60 11 A = = = tan 1 1
20 Practice Questions 2 1. For each of the following triangles, write down sin A, cos A and tan A. Give your answers in simplest form. Label the sides of the triangle: (iv) (Adj) Opp Hyp 3 3 6 5 33 65 = = = sin A Adj Hyp 5 6 6 5 56 65 = = = cos A (Opp) (Hyp) Opp Adj 3 3 5 6 33 56 = = = tan A
20 Practice Questions 2 1. For each of the following triangles, write down sin A, cos A and tan A. Give your answers in simplest form. Label the sides of the triangle: (v) (Opp) Opp Hyp 3 5 9 5 A = = = sin 3 Adj Hyp 6 9 2 3 A = = = cos (Hyp) (Adj) Opp Adj 3 5 6 5 A = = = tan 2
20 Practice Questions 2 1. For each of the following triangles, write down sin A, cos A and tan A. Give your answers in simplest form. Label the sides of the triangle: (vi) Opp Hyp 7 1 2 A = = = = sin (Opp) (Adj) 2 7 2 2 Adj Hyp 7 1 2 A = = = = cos 2 7 2 2 Opp Adj 7 7 A = = = tan 1 (Hyp)
20 Practice Questions 2 2. Find the measure of the missing side, in the triangle shown. Hence write down sin A, cos A and tan A. Give your answers in simplest form. Label the sides of the triangle: (Hyp) O2 + A2 = H2 O2 + (5 5)2 = (7 3)2 (Opp) O2 + 30 25 = 53 29 O2 = 23 04 O = 23 04 (Adj) O = 4 8
20 Practice Questions 2 2. Find the measure of the missing side, in the triangle shown. Hence write down sin A, cos A and tan A. Give your answers in simplest form. Opp Hyp 4 8 7 3 48 73 = = = sin A (Hyp) (Opp) 4 8 Adj Hyp 5 5 7 3 55 73 = = = cos A Opp Adj 4 8 5 5 48 55 = = = tan A (Adj)
20 Practice Questions 2 3. (i) Use your calculator to find the value of tan 45 . tan 45 = 1
20 Practice Questions 2 3. (ii) Hence find |PQ| Label the sides of the triangle: Opp Adj PQ A = tan (Hyp) = tan45 (Opp) 7 PQ = 1 7 = 7 cm PQ (Adj)
20 Practice Questions 2 3. (iii) Hence find |PR| Give your answer in surd form. |PR|2 = 72 + 72 |PR|2 = 49 + 49 |PR|2 = 98 7 cm PR = 98 PR = 7 2 cm
20 Practice Questions 2 4. The diagram shows a right-angled triangle ABC. Find |BC| (i) |BC|2 + 42 = 52 |BC|2 + 16 = 25 |BC|2 = 25 16 |BC|2 = 9 BC = 9 BC = 3
20 Practice Questions 2 4. The diagram shows a right-angled triangle ABC. (ii) Write down sin BAC, cos BAC and tan BAC Label the sides of the triangle: (Hyp) (Opp) Opp Hyp 3 5 BAC = = sin Adj Hyp 4 5 BAC = = cos (Adj) Opp Adj 3 4 BAC = = tan
20 Practice Questions 2 4. The diagram shows a right-angled triangle ABC. (iii) Show that tan BAC =sin BAC cos BAC tan BAC =sin BAC cos BAC 3 5 4 5 3 4 5 5 = Multiply top and bottom by 5 3 4=3 4
20 Practice Questions 2 cosA=3 5. A is an angle, such that 5 Without finding the angle A, find sin A and tan A. 3 5 Adj Hyp Step 1: A = = cos Find opposite side to angle A 32 + (opp)2 = 52 9 + (opp)2 = 25 (opp)2 = 25 9 (opp)2 = 16 (opp) = 4
20 Practice Questions 2 cosA=3 5. A is an angle, such that 5 Without finding the angle A, find sin A and tan A. Step 2: Opp Hyp 4 5 A = = sin Opp Adj 4 3 A = = tan 4
20 Practice Questions 2 B =12 6. B is an angle, such that sin 37 Without finding the angle B, find cos B and tan B. 122 + x2 = 372 12 37 Opp Hyp B = = sin 144 + x2 = 1369 x2 = 1369 144 x2 = 1225 x = 1225 x = 35 Opp Adj 12 35 Adj Hyp 35 37 B = = B = = tan cos
20 Practice Questions 2 is an angle, such that tanq =1 7. 3 (i) Without finding the angle , find sin and cos ( ) 2 H2=(1)2+ H2=1+3 H2=4 H = 4 H = 2 3 1 Opp Adj = = tan 3 Opp Hyp 1 2 = = sin Adj Hyp 3 = = cos 2
20 Practice Questions 2 is an angle, such that tanq =1 7. 3 (ii) Show that sin2A + cos2A = 1 sin2A + cos2A = (sin A)2 + (cos A)2 2 2 =1 3 + 2 2 1 4 3 4 4 4 = + = = 1 sin2A + cos2A = 1
20 Practice Questions 2 Use the information given in the diagram to show that sin + cos > tan 8. Opp Hyp =3 5 Adj Hyp Opp Adj =3 4 = = = Label the sides of the triangle: sin cos tan =4 5 (Hyp) 5 3 sin + cos =3 (Opp) 5+4 =7 5 5 4 (Adj) 7 5>3 4 sin + cos tan
20 Practice Questions 2 9. The diagram shows two right angled triangles. Find each of the following. Where appropriate, leave your answer in surd form. |SR| (i) S |SR|2 = 32 + 62 = 9 + 36 5 3 = 45 SR = 45 Q R P 6 = 9 5 =3 5
20 Practice Questions 2 9. The diagram shows two right angled triangles. Find each of the following. Where appropriate, leave your answer in surd form. |PQ| (ii) S |PQ|2 + 32 = 52 |PQ|2 + 9 = 25 5 3 |PQ|2 = 25 9 |PQ|2 = 16 Q R P 6 PQ = 16 = 4
20 Practice Questions 2 9. The diagram shows two right angled triangles. Find each of the following. Where appropriate, leave your answer in surd form. (iii) sin SRQ Label the sides of the triangle (Hyp) 3 5 (Opp) Opp Hyp 3 3 5 1 5 SRQ = sin 4 SRQ = sin (Adj) 5 SRQ = = sin 5
20 Practice Questions 2 9. The diagram shows two right angled triangles. Find each of the following. Where appropriate, leave your answer in surd form. (iv) tan SPQ Label the sides of the triangle (Hyp) (Opp) Opp Adj SPQ = tan 4 3 4 (Adj) SPQ = tan
20 Practice Questions 2 9. The diagram shows two right angled triangles. Find each of the following. Where appropriate, leave your answer in surd form. (v) cos RSQ Label the sides of the triangle (Hyp) 3 5 Adj Hyp 3 3 5 1 5 (Adj) RSQ = cos 4 RSQ = cos (Opp) 5 RSQ = = cos 5
20 Practice Questions 2 9. The diagram shows two right angled triangles. Find each of the following. Where appropriate, leave your answer in surd form. (vi) Investigate if SPR is right angled. ( 25 + 45=100 ) 2 (5)2+ 3 5 =(10)2 3 5 70 100 4 Therefore, SPR is not right-angled.
