Determine the exact value of the following trigonometric expression without the help of the calculator.

sin(sin^-1 0.7)

Transform the following expression into an algebraic expression. Use a right triangle in writing the algebraic expression. Assume that the inverse trigonometric function is defined for its argument and assume that x > 0.

tan (sin⁻¹ 2x)

Transform the following expression into an algebraic expression. Use a right triangle in writing the algebraic expression. Assume that the inverse trigonometric function is defined for its argument and assume that x > 0.

csc (sin⁻¹ (3/x))

Determine the exact value of the following trigonometric expression by sketching.

tan (cos^-1 (12/37))

Determine the exact value of the following trigonometric expression by sketching.

tan [cos^-1 (-2/5)]

Without using a calculator, determine the exact value of the expression:

tan (cos⁻¹ ((√2)/2))

Determine the exact value of the expression without using a calculator.

$\cos \left({\tan }^{-1}(-5)\right)$