Write the given expression as an algebraic expression in x.

$$\sin \left( 2 \tan ^ { -1 } x \right)$$

Simplify the expression. (a + b)² - (a - b)²

Simplify each expression. If the expression does not represent a real number, say so.

$$\sqrt { 0.0004 }$$

Write an algebraic expression for the word expression: the quotient of - 9 and y.

In this exercise, use a right triangle to write each expression as an algebraic expression. Assume that $x$ is positive and that the given inverse trigonometric function is defined for the expression in $x$.

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

Simplify each expression. If the expression does not represent a real number, say so.

$$\sqrt { 0.01 }$$

Use the Distributive Property to write each expression as an equivalent algebraic expression. $3.7(r - 1)$

Simplify each expression. If the expression does not represent a real number, say so.

$$\sqrt { - 64 }$$

Write the trigonometric expression as an algebraic expression. $\sin (2 \arcsin x)$

Find an algebraic expression equivalent to the given expression. [Hint: Form a right triangle]. $\cot (\arccos x)$

In this exercise, use a right triangle to write each expression as an algebraic expression. Assume that $x$ is positive and that the given inverse trigonometric function is defined for the expression in $x$.

$$\sin \left(\cos ^{-1} 2 x\right)$$

Write each expression as an algebraic (nontrigonometric) expression in u, u>0. tan(arccos u)

Write each expression as an algebraic expression in $u, u>0$.

$$\csc (\arctan \frac{\sqrt{9-u^2}}{u})$$

Use a right triangle to write each expression as an algebraic expression. Assume that x is positive and that the given inverse trigonometric function is defined for the expression in x.

$$\cos \left( \sin ^ { - 1 } 2 x \right)$$