0. Functions

Solve the following equations.

$\tan^22\theta=1,0\lt{\theta}\lt{\pi}$

Solve the following equations.

{Use of Tech} $\sin2\theta=\frac15,0\lt{\theta}\lt{\frac{\pi}{2}}$

Solving equations Solve each equation.

√2 sin 3Θ + 1 = 2, 0 ≤ Θ ≤ π

Solving equations Solve each equation.

sin² 2Θ = 1/2, -π/2 ≤ Θ ≤ π/2

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. Find a and b if c = 2, B = π/3.

b. Find a and c if b = 2, B = π/3.

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.

Two wires stretch from the top T of a vertical pole to points B and C on the ground, where C is 10 m closer to the base of the pole than is B. If wire BT makes an angle of 35° with the horizontal and wire CT makes an angle of 50° with the horizontal, how high is the pole?

Observers at positions A and B 2 km apart simultaneously measure the angle of elevation of a weather balloon to be 40° and 70°, respectively. If the balloon is directly above a point on the line segment between A and B, find the height of the balloon.

A hot-air balloon rising straight up from a level field is tracked by a range finder located 500 ft from the point of liftoff. Express the balloon’s height as a function of the angle the line from the range finder to the balloon makes with the ground.

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.

Evaluating trigonometric functions Without using a calculator, evaluate the following expressions or state that the quantity is undefined.

cos (2π/3)

Evaluating trigonometric functions Without using a calculator, evaluate the following expressions or state that the quantity is undefined.

tan (15π/4)

Evaluating trigonometric functions Without using a calculator, evaluate the following expressions or state that the quantity is undefined.

sec (7π/6)

Evaluating trigonometric functions Without using a calculator, evaluate the following expressions or state that the quantity is undefined.

sec (5π/2)

[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?