Exam 6: Analytic Trigonometry

Use a half-angle identity to find sin if csc x = and . Give the exact answer.

Solve the given trigonometric equation exactly over the interval, 0 $\le$ x $\le$ 2 $\pi$ .

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Write as a single trigonometric function.

Verify the identity

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

If a person breathes in and out every 3 seconds, the volume of air in their lungs can be modeled by , where A is in liters of air and x is in seconds. How many seconds into the cycle is the volume of air equal to 2.00 liters?

Solve the given trigonometric equation on 0° $\le$ $\theta$ $\le$ 360°and express answer in degrees to two decimal places.

Solve the given trigonometric equation exactly over the interval, 0 ≤ θ ≤ 2π.

Solve the trigonometric equation on 0° ≤ x ≤ 360°. Give answers in degrees and round to two decimal places.

Determine if is conditional or an identity.

The monthly sales of soccer balls is approximated by where x is the number of the month (January is x = 1, etc.) During which month do the sales reach 2346.4?

Find the exact value of if the terminal side of lies in I and the terminal side of lies in II.

Solve the given trigonometric equation exactly over the interval, 0 $\le$ x $\le$ 2 $\pi$ .

Evaluate the expression exactly if possible. If not possible, state why.

Area of a Triangle. A formula for finding the area of a triangle when given the measures of the angles and one side is area = ,where a is the length of the side opposite angle A. If the measures of angles B and C are 13 °and 71° , respectively, and if a = 9 feet, use the appropriate product-to-sum identity to change the formula so that you can solve for the area of a triangle. Round your answer to two decimal places.

The number of hours of daylight in San Diego, California, can be modeled with H(t) =12 + 2.4sin(0.017t - 1.377) where t is the day of the year (January 1, t = 1 etc) For what values of t is the number of hours equal to 14? Round to 2 decimal places.

If cos x = And sin x > 0, find tan 2x.

Solve the given trigonometric equation exactly over the interval, 0 $\le$ $\theta$ $\le$ 2 $\pi$ .

If a person breathes in and out every 3 seconds, the volume of air in their lungs can be modeled by , where A is in liters of air and x is in seconds. How many seconds into the cycle is the volume of air equal to 2.50 liters?