0. Functions

Given the right triangle below, evaluate $\(\cos\]\theta\)$.

Convert the angle $-\(\frac{5\pi}{6}\)$ from radians to degrees.

A point P in the first quadrant lies on the parabola 𝔂 = 𝔁². Express the coordinates of P as functions of the angle of inclination of the line joining P to the origin.

Convert the angle $540°$ from degrees to radians.

In Exercises 65–68, ABC is a right triangle with the right angle at C. The sides opposite angles A, B, and C are a, b, and c, respectively.

a. Express sin A in terms of a and c.

b. Express sin A in terms of b and c.

[Technology Exercise]

You want to make an 80° angle by marking an arc on the perimeter of a 12-in.-diameter disk and drawing lines from the ends of the arc to the disk’s center. To the nearest tenth of an inch, how long should the arc be?

Identify what angle, $\(\theta\)$ , satisfies the following conditions.

$\(\cos\]\theta\)=\(\frac{\sqrt3}{2}\)$; $\(\sin\]\theta\)$ < $0$

Solve the following equations.

$\(\cos\)3x=\(\sin\)3x,0\(\leq{x}\]\lt\)2\(\pi\)$

In Exercises 39–42, express the given quantity in terms of sin x and cos x.

sin (2π − x)

Wave velocity Use Exercise 73 to do the following calculations.

a. Find the velocity of a wave where λ = 50 m and d = 20 m.

Rewrite the expressions in Exercises 5–10 in terms of exponentials and simplify the results as much as you can.

8. cosh(3x) - sinh(3x)

Each of Exercises 1–4 gives a value of sinh x or cosh x. Use the definitions and the identity cosh²x - sinh²x = 1 to find the values of the remaining five hyperbolic functions.

1. sinh x = -3/4

Each of Exercises 1–4 gives a value of sinh x or cosh x. Use the definitions and the identity cosh²x - sinh²x = 1 to find the values of the remaining five hyperbolic functions.

2. sinh x = 4/3

Rewrite the expressions in Exercises 5–10 in terms of exponentials and simplify the results as much as you can.

6. sinh(2ln x)

Evaluating hyperbolic functions Evaluate each expression without using a calculator or state that the value does not exist. Simplify answers as much as possible.

a. cosh 0