%3D In the right triangle shown, explain why v = (x/2)- u. Explain how you can obtain all six cofuncti %3D Note that u and v are complementary angles. So the cofunction identities state that "a trigonometri- Label the side opposite v as a, the side opposite u as b, and the hypotenuse as c. Since u + Next, express all six trigonometric functions for each angle. sin - u) cos(u) = sin(v) » cos(u) %3D %3D co(-u) sin(u) : - sin(u) = cos %3D tan(u) = cot(v) = tan(u) = cot-u) %3D %3D sec(u)3D등- - sec(u) = cse( -u) %3! = CS csc(u) = sec(v) csc(u) = sec %3D cot(u) = - cot(u) = tan-u) %3D
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.
![In the right triangle shown, explain whyv (x/2)-u. Explain how you can obtain all six cofunction identities from this triangle for 0 <u< T/2.
Note that u and v are complementary angles. So the cofunction identities state that "a trigonometric function of an angle u is equal to the corresponding cofunction of the complementary angle
Label the side opposite v as a, the side opposite u as b, and the hypotenuse as c. Since u + v +
I, u+v=
and v =
-U.
Next, express all six trigonometric functions for each angle.
cos(u) =
= sin(v) cos(u) = sin
- sin(u) = cos- u)
sin(u) =
=COS
co-)
tan(u) =
cot(v) tan(u) = co
sec(u) = =
→sec(u)-csc(즉-)
= sec(v)
- csc(u) = sec-u)
csc(u) =
%3D
cot(u) =
= cot(u)
= tan](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc222fad-aaa8-448d-8fdf-d2fe3f914fce%2F4e0f487b-c7f2-4614-9b84-ec777e796595%2Fcr2gzwm_processed.jpeg&w=3840&q=75)
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