Find the principal value of cosβ1 (π/π).
Let y = cos-1 (1/2)
Hence,
cos y = 1/2
cos y = cos (π/3)
Range of principal value
of cosβ1 is between 0 & Ο
Hence principal value is π /π
Rough
We know that cos 60Β° = 1/2
ΞΈ = 60Β° = 60 Γ π/180
= π/3
Since 1/2 is positive
Principal value is ΞΈ i.e. π/3
Find the principal value of cosβ1 ((βπ)/π).
Let y = cos-1 ((β1)/2)
Hence,
cos y = (β1)/2
cos y = cos (πβπ/3)
cos y = cos (2π/3)
Range of principal value
of cosβ1 is between 0 & Ο
Hence principal value is ππ /π
Rough
We know that cos 60Β° = 1/2
ΞΈ = 60Β° = 60 Γ π/180
= π/3
Since (β1)/2 is negative
Principal value is Ο β ΞΈ i.e. πβπ/3
Find the principal value of sinβ1 (π/π).
Let y = sin-1 (1/2)
Hence,
sin y = 1/2
sin y = sin (π/6)
Range of principal value
of sin β1 is between (βπ)/2 and ( π)/2
Hence principal value is π /π
Rough
We know that sin 30Β° = 1/2
ΞΈ = 30Β° = 30 Γ π/180
= π/6
Since 1/2 is positive
Principal value is ΞΈ i.e. π/6
Find the principal value of sinβ1 ((βπ)/π).
Let y = sin-1 ((β1)/2)
Hence,
sin y = (β1)/2
sin y = sin ((βπ)/6)
Range of principal value
of sin β1 is between (βπ)/2 and ( π)/2
Hence principal value is (βπ )/π
Rough
We know that sin 30Β° = 1/2
ΞΈ = 30Β° = 30 Γ π/180
= π/6
Since (β1)/2 is negative
Principal value is βΞΈ i.e. (βπ)/6
Find the principal value of tanβ1 (1).
Let y = tan-1 (1)
Hence,
tan y = 1
tan y = tan (π/4)
Range of principal value
of tan β1 is between (βπ)/2 and ( π)/2
Hence principal value is π /π
Rough
We know that tan 45Β° = 1
ΞΈ = 45Β° = 45 Γ π/180
= π/4
Since 1 is positive
Principal value is ΞΈ i.e. π/4
Find the principal value of tanβ1 (β1).
Let y = tan-1 (β1)
Hence,
tan y = β1
tan y = tan ((βπ)/4)
Range of principal value
of tan β1 is between (βπ)/2 and ( π)/2
Hence principal value is (βπ )/π
Rough
We know that tan 45Β° = 1
ΞΈ = 45Β° = 45 Γ π/180
= π/4
Since 1 is positive
Principal value is βΞΈ i.e. (βπ)/4
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.