Write the following trigonometric expression as an algebraic expression containing u and v. Give the restrictions required on u and v. sin ( cos^-1 u sin^-1 v)

--- restriction

Step-by-step explanation:

Given

Required

Write in terms of u and v

Let:

Take arc cos of both sides

Using the following trigonometry identity

So:

Take square roots of both sides

So, we have:

Let:

Take arc cos of both sides

So:

Take square roots

So, we have:

So, we have:

Apply sine rule

Expand

The restriction on u and v is:

b. 2 and 4

step-by-step explanation:

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2