Trigonometry

Learning Target C2: I can find complex solutions to algebraic equations. Given real / complex zeros, write the polynomial function having those zeros. Find all solutions to the polynomial equations 1. x²2x+2=0 2. 16t24t+3=0

Solve for in the equation: tanθ=-0.6319, 0 ≤ θ ≤ 360. Give answers to the nearest degree.

Determine the value of 2(sin 45 )(cos 45')-4(sin 30') (cos 60') by substituting in the exact special angle values.

5. Use the function f(x) = cos (2x + 2π/3) - 4, to answer the questions which follow. a) Amplitude: b) Period: c) Phase Shift: d) Equation of the Axis: e) Domain: f) Range: g) Use transformations to sketch and label and accurate graph of f(x).

4. One cycle of a graph of a cosine function begins at a maximum point (- , 10), passes through the minimum point (2), before reaching the next maximum_point (2π,10). Determine a possible function (equation) to represent this function.

3. Determine two possible equations, one of the form g(x) = asin[k(x - d)] + c and the other of the form g(x) = acos[k(x - d)] + c to represent the graph of the sinusoidal function shown below.

1. By showing all steps and without using a calculator, determine the exact values for each of the following. Make use of compound and double angle formulas.

\text { Find the exact value of } \sec \left(\tan ^{-1}\left(-\frac{4}{9}\right)\right)

a) Draw one of the primary trigonometric functions on the domain [0, 27]. Then also draw its reciprocal function. b) List the locations of vertical asymptotes, locations of zeros, locations of minimums of your two functions drawn in 2(a).

3. Darcy mounted a motion sensor so it would light a path to the door on her deck. If you know AB = 10 feet, and BE and BD trisect ZABC, what is the perimeter of the deck area to the right of the beam of light (ABDC)? Part 1: What other angles or sides of ABDC can you label given that side AB is 10 feet,BE and BD trisect ZABC? Label the diagram accordingly, and explain your reasoning. (4points) Part 2: Use the trigonometric ratios 30° and 60° to calculate and label the remaining sides of ABDC. Show your work. (3 points) Part 3: Use the Pythagorean Theorem to calculate the length of side BD. Does this method verify the length you found using trigonometric ratios? (2 points) Part 4: What is the perimeter of the area to the right of the beam of light on Darcy's deck(ABDC)? Show your work. Use your calculator to round your final answer to the nearest foot. (3 points)