1-A point P(x, y) is shown on the unit circle U corresponding to a real number t. Find the values of the trigonometric functions at t. sin t = cos t = tan t = csc t = sec t = cot t = 2-Let P(t) be the point on the unit circle U that corresponds to t. If P(t) has the given rectangular coordinates, find the following. 3 5 , 4 5 (a) P(t + ) (x, y) = (b) P(t ) (x, y) = (c) P(t) (x, y) = (d) P(t ) (x, y) = 3-Let P be the point on the unit circle U that corresponds to t. Find the coordinates of P and the exact values of the trigonometric functions of t, whenever possible. (If an answer is undefined, enter UNDEFINED.) (a) t = 5/2 P(x, y) = sin(5/2) = cos(5/2) = tan(5/2) = csc(5/2) = sec(5/2) = cot(5/2) = (b) t = /2 P(x, y) = sin(/2) = cos(/2) = tan(/2) = csc(/2) = sec(/2) = cot(/2) = 4-Use a formula for negatives to find the exact value. (a) sin(270) (b) cos 3 4 (c) tan(45) 5-Determine whether the equation is an identity for all values of x where the functions are defined. cos (x) sec (x) = tan x Yes, it is an identity. No, it is not an identity. 6-Complete the statement by referring to a graph of a trigonometric function. (a) As x (/4), cot x . (b) As x (3), cot x . 7-Refer to the graph of y = sin x or y = cos x to find the exact values of x in the interval [0, 4] that satisfy the equation. (Enter your answers as a comma-separated list.) cos x = 1 x = 8-Refer to the graph of y = tan x to find the exact values of x in the interval (/2, 3/2) that satisfy the equation. (Enter your answers as a comma-separated list.) tan x = 0 x = 9-Find the reference angle R if has the given measure. (a) 5/4 R = (b) R = 2/3 (c) 5/6 R = (d) 13/4 R = 10-Find the exact value. (a) sin 240 (b) sin(300) 11-Approximate to three decimal places. (a) sec 7150' (b) csc 0.31 12-Approximate the acute angle to the following. cos = 0.3620 (a) the nearest 0.01 (b) the nearest 1' ' 13-Approximate to four decimal places. (a) sin 8340' (b) cos 514.7 (c) tan 3 (d) cot 15840' (e) sec 1016.1 (f) csc 0.42 14-Approximate, to the nearest 0.01 radian, all angles in the interval [0, 2) that satisfy the equation. (Enter your answers as a comma-separated list.) (a) sin = 0.4292 = (b) cos = 0.1403 = (c) tan = 3.2203 = (d) cot = 2.6918 = (e) sec = 1.7153 = (f) csc = 4.8729 = 15-Find the amplitude and the period and sketch the graph of the equation. (a) y = 3 cos x amplitude period (b) y = cos 8x amplitude period (c) y= 1 4 cos x amplitude period (d) y = cos 1 6 amplitude period x (e) y = 2 cos 1 6 x amplitude period (f) y= 1 4 amplitude period cos 4x (g) y = 2 cos x amplitude period (h) y = cos(6x) amplitude period 16-Find the amplitude, the period, and the phase shift. y = 4 sin 3x amplitude period phase shift Sketch the graph of the equation. 17-Find the amplitude, the period, and the phase shift. y = 4 cos 2x + 3 amplitude period phase shift Sketch the graph of the equation. 18-The graph of a sine function with a positive coefficient is shown in the figure. (a) Find the amplitude, period, and phase shift. (The phase shift is the first negative zero that occurs before a maximum.) amplitude period phase shift (b) Write the equation in the form y = a sin(bx + c) for a > 0, b > 0, and the least positive real number c. 19-Find the period. y= 1 6 tan 4x 7 Sketch the graph of the equation. Show the asymptotes. 20-Find the period. y = 6 sec 6x 6 Sketch the graph of the equation. Show the asymptotes. 21-Use the graph of a trigonometric function to aid in sketching the graph of the equation without plotting points. y = 9|sin x| + 10