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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
AB^{2} = AD^{2} + BD^{2}
= (30√3)^{2} + 30^{2}
= 60^{2}
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 30^{0} [∵ sin 30^{0} = ½]
∴ α = 30^{0}
We have tan β = √3
tan β = tan 60^{0}
∴ β = 60^{0}
Now In ΔABC
∠ABC + ∠BCA + ∠CAB = 180^{0}
∠ABC + 60^{0} + 30^{0} = 180^{0}
∠ABC = 90^{0}
∴ ∠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^{–1}x; 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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