0. Functions

132. What is special about the functions

f(x) = arcsin((1/√(x²+1)) and g(x)=arctan(1/x)?

Explain.

Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.

6. b. arccsc(-2/√3)

Evaluate the expression using a calculator. Express your answer in radians, rounding to two decimal places.

$\(\sin\)^{-1}\(\left\)(-\(\frac\)13\(\right\))$

Evaluate the expression.

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

An inverse tangent identity

b. Prove that tan⁻¹ x + tan⁻¹ x(1/x) = π/2, for x > 0.

Evaluate the expression.

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

Evaluate the expression.

$\(\cos\)^{-1}\(\left\)(-\(\frac{\sqrt2}{2}\]\right\))$

Inverse sines and cosines Evaluate or simplify the following expressions without using a calculator.

cos (cos⁻¹ ( -1 ))

Express $\(\theta\)$ in terms of $x$ using the inverse sine, inverse tangent, and inverse secant functions. <IMAGE>