Trigonometric Ratios (sine, Cosine, and Tangent Ratios) Worksheet

Trigonometric Ratios (sine, Cosine, and Tangent Ratios) Worksheet
  • Page 1
 1.  
What is the value of sin 45o - cos 45o?
a.
1
b.
2
c.
3


Solution:

From the trigonometric tables sin 45o = 0.7071 and cos 45o = 0.7071

sin 45o - cos 45o = 0.7071 – 0.7071 = 0
[Substitute the values of sin 45o and cos 45o.]

The value of sin 45o - cos 45o = 0.


Correct answer : (4)
 2.  
Round the value of sin 36o to the nearest hundredth.
a.
0.59
b.
0.69
c.
0.68
d.
0.81


Solution:

sin 36o = 0.58778525229247312916870595463907
[Find using calculator.]

The value of sin 36o is approximately equal to 0.59.
[Rounded to nearest hundredth.]


Correct answer : (1)
 3.  
sin A =
a.
(Side adjacent to A)/Side opposite to A
b.
Hypotenuse/Side opposite to A
c.
(Side opposite to A)/Hypotenuse
d.
(Side opposite to A)/Side adjacent to A


Solution:

sin A = (Side opposite to A)/(Hypotenuse)


Correct answer : (3)
 4.  
What is the value of tan R in the figure?


a.
3 5
b.
4 3
c.
3 4
d.
5 3


Solution:

tan R = (Opposite side of R)/(Adjacent side of R).

Opposite side of R = PQ = 3
adjacent side of RP = 4

In ΔABC, tan R = PQ / RP

tan R = 3 / 4
[Substitute the values of PQ and RP.]


Correct answer : (3)
 5.  
What is the length of side RP in ΔPQR?

a.
1 foot
b.
4 feet
c.
6 feet
d.
3 feet


Solution:

From the figure, PQ = 6 feet and Q = 45o.

In the figure, RP and PQ are opposite and adjacent sides of angle Q respectively.

tan Q = Opposite side/Adjacent side.

In ΔPQR, tan Q = RP / PQ

tan 45o = RP / 6
[Substitute the values of Q and PQ.]

1 = RP / 6
[Substitute the value of tan 45o from table.]

RP = 6
[Simplify.]

The length of side RP is 6 feet.


Correct answer : (3)
 6.  
What is the length of AC, if the side of each small square is 1 unit?

a.
6√2 units
b.
6 units
c.
8√2 units
d.
4√2 units


Solution:

sin θ = Opposite side/Hypotenuse.

sin 45o = BC / AC
[From the figure.]

From the figure, BC = 4 units

sin 45o = 4 / AC
[Substitute BC.]

1 / √2 = 4 / AC
[sin 45o = 1 / √2]

AC = 4√2
[Cross multiply.]

So, the length of AC is 4√2 units.


Correct answer : (4)
 7.  
ABC is a right triangle. What is the measure of ACB, if AB = 2 cm and AC = 4 cm?


a.
30o
b.
60o
c.
45o
d.
15o


Solution:

Let ACB = q

In a right triangle, sin q = opposite side / hypotenuse
[Write the formula for the sin ratio.]

= ABAC
[Since the opposite side to ACB is AB and the hypotenuse of the triangle is AC.]

= 24 = 12
[Substitute AB = 2 and AC = 4 and simplify.]

= Sin 30o

So, ACB = 30o.


Correct answer : (1)
 8.  
Find the value of a, if ΔABC is a right triangle.


a.
8.71
b.
9.2
c.
10
d.
6.25


Solution:

sin A = opposite / hypotenuse
[Choose an appropriate trigonometric ratio.]

sin A = BC / AC

sin 35o = 5 / a
[Substitute the values.]

a x sin 35o = 5
[Multiply each side by a.]

a x sin 35o/sin 35o = 5/sin 35o
[Divide each side by sin 35o.]

a = 5/sin 35o
[Simplify.]

a = 5 / 0.5735
[Use table or calculator to find the value of sin 35o.]

a = 8.71
[Divide.]

The value of a is 8.71.


Correct answer : (1)
 9.  
A vertical pole is 70 m high. Find the angle formed by the pole at a point 70 m away from its base.


a.
30o
b.
75o
c.
60o
d.
45o


Solution:

Let AB be the height of the pole.

The height of the pole, AB = 70 m

Let BC be the distance from the base of the pole to the point where the angle is to be measured. So, BC = 70 m

tan C = opposite side/adjacent side
[Choose an appropriate trigonometric ratio.]

From ΔABC, tan C = AB / BC

tan C = 7070 = 1
[Substitute and simplify.]

From the trigonometric tables, tan 45o = 1

So, the angle formed by the pole at the point 70 m away from its base is 45o.
[As tan C = 1 and tan 45o = 1, C = 45o.]


Correct answer : (4)
 10.  
What is the value of sin A in the figure?


a.
12 13
b.
5 13
c.
13 5
d.
13 12


Solution:

sin A = (Side opposite to A)/Hypotenuse

In the triangle, BC is the side opposite to A and AC is the hypotenuse.

sin A = BCAC

= 513
[Substitute BC = 5 and AC = 13.]


Correct answer : (2)

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