Test: Inverse Trigonometric Functions- Case Based Type Questions
15 Questions MCQ Test Mathematics (Maths) Class 12 | Test: Inverse Trigonometric Functions- Case Based Type Questions
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Direction: Read the following text and answer the following questions on the basis of the same:
Two men on either side of a temple of 30 metres high observe its top at the angles of elevation α and β respectively. (as shown in the figure above). The distance between the two men is 40√3 metres and the distance between the first person A and the temple is 30√3 meters.
∠CAB = α =
sin α = BD/AB
AB2 = AD2 + BD2
= (30√3)2 + 302
= 602
AB = 60 m
Now, sinα = 30/60
Sinα = ½
I.e. ∠CAB = α = sin-1(½)
Direction: Read the following text and answer the following questions on the basis of the same:
Two men on either side of a temple of 30 metres high observe its top at the angles of elevation α and β respectively. (as shown in the figure above). The distance between the two men is 40√3 metres and the distance between the first person A and the temple is 30√3 meters.
Domain and Range of cos−1 x =
Domain of cos−1 x includes -1 and 1
Range of cos−1 x also includes 0 and π
Direction: Read the following text and answer the following questions on the basis of the same:
In the school project Sheetal was asked to construct a triangle and name it as ABC. Two angles A and B were given to be equal to tan-1(½) and tan-1(⅓) respectively.
The value of sin A is _______.
A = tan-1(½)
⇒ tan A = ½
∴ sin A = 1/√5
Direction: Read the following text and answer the following questions on the basis of the same:
In the school project Sheetal was asked to construct a triangle and name it as ABC. Two angles A and B were given to be equal to tan-1(½) and tan-1(⅓) respectively.
The third angle, ∠C = _______.
= π - (π/4)
= 3π/4
Direction: Read the following text and answer the following questions on the basis of the same:
The value of an inverse trigonometric functions which lies in the range of Principal branch is called the principal value of that inverse trigonometric functions.
Principal value of sin–1 (½) is
sin y = ½
Principal value branch of sin–1 is (-π/2, π/2)
and sin(π/6) = ½
⇒ Principal value of sin-1(½) is π/6.
Direction: Read the following text and answer the following questions on the basis of the same:
The value of an inverse trigonometric functions which lies in the range of Principal branch is called the principal value of that inverse trigonometric functions.
Principal value of 2cos–1 (1) + 5tan–1 (1) is:
= 2 x 0 + 5 x π/4
= 5π/4
Direction: Read the following text and answer the following questions on the basis of the same:
Two men on either side of a temple of 30 metres high observe its top at the angles of elevation α and β respectively. (as shown in the figure above). The distance between the two men is 40√3 metres and the distance between the first person A and the temple is 30√3 meters.
∠CAB = α =
Cosα = AD/AB
Cosα = 30√3/60
α = cos-1(√3/2)
∴∠CAB = α = cos-1(√3/2)
Direction: Read the following text and answer the following questions on the basis of the same:
In the school project Sheetal was asked to construct a triangle and name it as ABC. Two angles A and B were given to be equal to tan-1(½) and tan-1(⅓) respectively.
cos(A + B + C) = _______.
∴ A + B + C = 180°
cos (A + B + C) = cos 180°
= -1
Direction: Read the following text and answer the following questions on the basis of the same:
The value of an inverse trigonometric functions which lies in the range of Principal branch is called the principal value of that inverse trigonometric functions.
Principal value of tan–1 (1)
= π/4
Direction: Read the following text and answer the following questions on the basis of the same:
Two men on either side of a temple of 30 metres high observe its top at the angles of elevation α and β respectively. (as shown in the figure above). The distance between the two men is 40√3 metres and the distance between the first person A and the temple is 30√3 meters.
∠BCA = β =
= 40√3 - 30√3
= 10√3 m
In ΔBDC
Direction: Read the following text and answer the following questions on the basis of the same:
In the school project Sheetal was asked to construct a triangle and name it as ABC. Two angles A and B were given to be equal to tan-1(½) and tan-1(⅓) respectively.
If B = cos–1 x, then x = _______.
⇒ tan B = ⅓
∴ cos B = 3/√10
B = cos-1(3/√10)
⇒ x = 3/√10
Direction: Read the following text and answer the following questions on the basis of the same:
The value of an inverse trigonometric functions which lies in the range of Principal branch is called the principal value of that inverse trigonometric functions.
Principal value of cot-1(√3) is :
Direction: Read the following text and answer the following questions on the basis of the same:
Two men on either side of a temple of 30 metres high observe its top at the angles of elevation α and β respectively. (as shown in the figure above). The distance between the two men is 40√3 metres and the distance between the first person A and the temple is 30√3 meters.
∠ABC =
Sin α = ½
i.e., sin α = sin 300 [∵ sin 300 = ½]
∴ α = 300
We have tan β = √3
tan β = tan 600
∴ β = 600
Now In ΔABC
∠ABC + ∠BCA + ∠CAB = 1800
∠ABC + 600 + 300 = 1800
∠ABC = 900
∴ ∠ABC = π/2
Direction: Read the following text and answer the following questions on the basis of the same:
In the school project Sheetal was asked to construct a triangle and name it as ABC. Two angles A and B were given to be equal to tan-1(½) and tan-1(⅓) respectively.
If A = sin–1x; then the value of x is:
⇒ tan A = ½
∴ Sin A = 1/√5
A = sin-1(1/√5)
⇒ x = 1/√5
Direction: Read the following text and answer the following questions on the basis of the same:
The value of an inverse trigonometric functions which lies in the range of Principal branch is called the principal value of that inverse trigonometric functions.
Principal value of sin -1(1) + sin-1(1/√2) is
= 3π/4
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