# 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 general formula for the nth term, ,, for the following sequences. (a) 26, 23, 20, 17,... (b) 6, 12, 24, 48, ...

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

Simplify. State any restrictions on the variables.

Simplify 2m² + 5m / m² +4m-21 + 2m² +13m +20 / m² +m-12 State any restrictions on the variables.

Determine the equation of the inverse of f(x)=2(x-5)²-3.

Learning Target Cl: I can perform operations on complex numbers. Perform the requested operation:

Find x so that function f (x) = lg (√x² – 12x +11) is defined.

2560 mg of a certain radioactive element is stored in a laboratory for 136 days. At the end of this period only 10 mg of the element remain. What is the half-life of this element? (An algebraic solution is required)

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