(a) To define the inverse sine function, we restrict the domain of sine to the interval On this interval the sine function is one-to-one, and its inverse function sin- is defined by sin-(x) = y e sin . For example, sin- because sin = (b) To define the inverse cosine function, we restrict the domain of cosine to the interval On this interval the cosine function is one-to-one and its inverse function cos- is defined by cos-(x) = y ee cos For example, cos because cos
Trigonometric Identities
Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.
Inverse Trigonometric Functions
Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec). When trigonometric ratios are calculated, the angular values can be calculated with the help of the inverse trigonometric functions.
![(a) To define the inverse sine function, we restrict the domain of sine to the interval
On this interval the sine function is one-to-one, and its inverse function sin-1 is defined by
sin-(x) = y A sin
. For example, sin
because sin
():-
(b) To define the inverse cosine function, we restrict the domain of cosine to the interval
On this interval the cosine function is one-to-one and its inverse function cos-1 is defined by
]-I
cos-1(x) =
For example, cos
because cos
y e cos](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe486ef45-9c28-49a6-849c-e84f93e2f047%2F33f85a7d-8f18-44f7-858e-786b679f0f7e%2Fvknd30s8_processed.png&w=3840&q=75)
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