Trigonometry

I can state the multiple angle formulas for sine and cosine, and the power reduction formulas for sine and cosine. I can apply the multiple angle and product-to-sum formulas.

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

1. Given the relation {(1,-4), (2,0), (3,4), (2,6)), (a) State the domain. (b) State the range. (c) Is the relation a function? (Answer 'yes' or 'no') 2. If f(x)=x²-3x, evaluate f(-4). 3. Given f(x) = -2(x-7)² +5, (a) Does f(x) open up or does it open down? (b) State the coordinates of the vertex. 4. What is the y-intercept of y= 5(2¹)? 5. What is the principal angle of -71¹? 6. What is the range of y = √x? 7. Express √99 as a mixed radical in simplest form. 8. 753' is coterminal with what angle between 0 and 360? 9. What is the amplitude of y=-6cose? 10. What is the phase shift of y=sin(θ+30°)? 11. What is the period of y=sin 5θ? 12. What is the vertical shift of y=3cos(θ-90')-5? 13. Simplify m^-2 (m^-3)^5 / m^19 14. Evaluate 81^3/4

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.

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

Find the equation of the tangent line drwn for the function y = cos (2x) + cos(x) whne x = π /2

For what value(s) of k does the equation 5x²-kx+5=0 have no roots?

Learning Target AT2: I can verify a trigonometric identity. Verify each identify below. Begin with only one side and work to the other, as in class, the textbook, and the homework. All arguments must be 100% notationally correct, with equals signs along each line. Any omissions or errors on this element will result in an N grade. The derivation of the identity must use correct algebra throughout and result in a correct answer. 1. 2. sec a cot x + tan x 1 - 2 cos²0 sin cos = sin x = tan cot 0 Learning Target AT3: I can solve trigonometric equations giving all possible answers on a specified domain. Solve each of the following equations, providing the answers as requested. 1. Solve and give all solutions in the interval [0, 27) sin x 2 sin x cos x = 0 2. Solve and give all solutions in the interval [0, 27) cos x 1 = √3 sin x