Trigonometric & Polar Functions unit test
A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.
Converting degrees and radians
Range of arccos
Asymptotes of cosecant
Arc length and sector area
Reading midline from max and min
Symmetry of polar graphs
Law of sines
Choosing between the two triangle laws
Finding where a polar curve crosses the origin
Zeros of r
Solving trig equations
Quadratic in a trig function
Short answer 1. Define or explain: Range of secant and cosecant
3 ptsShort answer 2. Define or explain: Generating all solutions from a reference angle
3 ptsShort answer 3. Define or explain: Why b and period are reciprocal
3 ptsShort answer 4. Define or explain: Reading amplitude from max and min
3 ptsFree response
6 ptsSYMBOLIC MANIPULATIONS (Question 4, no calculator, 6 points). Determine exact values without a calculator; combine terms using rules for exponents and logarithms; show the work leading to your answers. Angle measures are in radians.
A. The functions g and h are given by g(x) = e²ˣ and h(x) = log₂(5x). A(i). Solve g(x) = 1/e⁶ for values of x in the domain of g. A(ii). Solve h(x) = 3 for values of x in the domain of h.
B. The functions j and k are given by j(x) = 7⁽³ˣ⁺¹⁾·7ˣ and k(x) = sin(2x)·sec x. B(i). Rewrite j(x) as an expression of the form 7^(expression). B(ii). Rewrite k(x) as an expression in which sin x appears exactly once and no other trigonometric functions are involved.
C. The function m is given by m(x) = tan²(3x). Find all input values for m in the interval [0, π/2] that yield an output value of 1.