7.1 Solving Trigonometric Equations with Identities Name: Syd Hendricks #1 Points possible: 1. Total attempts: 3 Simplify sec(t) cos(t) sin(t) to a single trig function. #2 Points possible: 1. Total attempts: 3 Simplify cot(t) csc(t) to a single trig function. #3 Points possible: 1. Total attempts: 3 Simplify cos(t)tan(t) to a single trig function. #4 Points possible: 1. Total attempts: 3 Simplify csc2 (t) csc2 (t) 1 to an expression involving a single trig function with no fractions. #5 Points possible: 1. Total attempts: 3 Simplify 1 + cot(t) 1 + tan(t) to a single trig function. #6 Points possible: 1. Total attempts: 3 Fill in the blanks: 1. If tan x = 1 then tan( x) = 2. If sin x = 0.3 then sin( x) = 3. If cos x = 0.4 then cos( x)= 4. If tan x = 1.5 then tan( + x)= #7 Points possible: 1. Total attempts: 3 Simplify to an expression involving a single trigonometric function with no fractions. cot( x)cos( x) + sin( x) #8 Points possible: 1. Total attempts: 3 Simplify and write the trigonometric expression in terms of sine and cosine: tan2 x sec2 x = . #9 Points possible: 1. Total attempts: 3 Determine the value of sin2 x + cos2 x for x = 80 degrees. 1 #10 Points possible: 1. Total attempts: 3 Simplify sin2 (t) + cos2 (t) sin2 (t) to an expression involving a single trig function with no fractions. Assignment 7.2 Sum and Difference Identities Name: Syd Hendricks #1 Points possible: 1. Total attempts: 3 Use an addition or subtraction formula to write the expression as a trigonometric function of one number: 3 2 3 2 B cos cos + sin sin = cos = . 7 7 21 21 2 A A= 3 , B= 1 . #2 Points possible: 1. Total attempts: 3 Use an addition or subtraction formula to write the expression as a trigonometric function of one number: tan 79 tan 19 = tan A = B. 1 + tan 79 tan 19 A = 60 , B= 3 . #3 Points possible: 1. Total attempts: 3 If sin(x + y) sin(x y) = 2f(x)sin y, then f(x) = cos x . #4 Points possible: 1. Total attempts: 3 Use an addition or subtraction formula to find the exact value of sin 165 = A= B= ; . A(B 1) . 4 #5 Points possible: 1. Total attempts: 3 Use an addition or subtraction formula to find the exact value of tan 75 = A= B= ; . #6 Points possible: 1. Total attempts: 3 Rewrite cos(x + 11 ) in terms of sin(x) and cos(x). 6 A + 1 B 1 . #7 Points possible: 1. Total attempts: 3 19 Use an addition or subtraction formula to find the exact value of sin( ) = 12 A= ; B= . A(B + 1) . 4 #8 Points possible: 1. Total attempts: 3 Use an addition or subtraction formula to find the exact value of cos( )= 12 A= ; B= . A(B + 1) 4 #9 Points possible: 1. Total attempts: 3 Find the exact value of sin(255 ). #10 Points possible: 1. Total attempts: 3 Simplify sec( x) to a single trig function using a sum or difference of angles identity. 2 . Assignment 7.3 Double-Angle, Half-Angle, and Reduction Formulas #1 Points possible: 1. Total attempts: 3 If csc(x) = 4, for 90 < x < 180 , then sin( x )= 2 cos( x )= 2 tan( x )= 2 #2 Points possible: 1. Total attempts: 3 Using a double-angle or half-angle formula to simplify the given expressions. (a) If cos2 (25 ) sin2 (25 ) = cos(A ), then A= degrees (b) If cos2 (2x) sin2 (2x) = cos(B), then B= . #3 Points possible: 1. Total attempts: 3 4 , csc x < 0, then 5 sin 2x = ; cos 2x = ; tan 2x = . If cos x = #4 Points possible: 1. Total attempts: 3 If sin x = sin 2x = cos 2x = tan 2x = 3 , x in quadrant III, then 5 ; ; . Name: Syd Hendricks #5 Points possible: 1. Total attempts: 3 If tan x = sin(2x) = cos(2x) = tan(2x) = 1 , cos x > 0, , then 3 ; ; . #6 Points possible: 1. Total attempts: 3 Use a half angle formula to fill in the blanks in the identity below: (cos(2x))2 = + cos( x) #7 Points possible: 1. Total attempts: 3 Use half angle formulas to fill in the blanks in the identity below: 4 (sin(5x)) = 1 cos( 2 x )+ 1 cos( 8 x) #8 Points possible: 1. Total attempts: 3 If sin 15 = A= B= 1 A B, then, by using a half-angle formula, find 2 , . #9 Points possible: 1. Total attempts: 3 If cos 22.5 = A= B= 1 A + B, then, by using a half-angle formula, find 2 , . #10 Points possible: 1. Total attempts: 3 = A B, then, by using a half-angle formula, find 8 A= , B= . If tan Assignment 7.5 Solving Trigonometric Equations Name: Syd Hendricks #1 Points possible: 1. Total attempts: 3 Solve sin(x) = 0.19 on 0 x < 2. There are two solutions, A and B, with A < B. A= B= Give your answers accurate to 3 decimal places. #2 Points possible: 1. Total attempts: 3 Solve 6 cos(3x) = 3 for the smallest three positive solutions. Give your answers accurate to at least two decimal places, as a list separated by commas. #3 Points possible: 1. Total attempts: 3 Find all solutions to 2 cos() = 3 on the interval 0 < 2. = Give your answers as exact values in a list separated by commas. #4 Points possible: 1. Total attempts: 3 Solve for t, 0 t < 2. 36 sin(t)cos(t) = 4 sin(t) t= Give your answers as values rounded to at least two decimal places in a list separated by commas. #5 Points possible: 1. Total attempts: 3 Solve 2 cos2 (w) 5 cos(w) + 2 = 0 for all solutions 0 w < 2. w= Give your answers as values accurate to at least two decimal places in a list separated by commas. #6 Points possible: 1. Total attempts: 3 Solve cos2 (x) = 8 sin(x) for all solutions 0 x < 2. x= Give your answers as values accurate to at least two decimal places in a list separated by commas. #7 Points possible: 1. Total attempts: 3 Solve 5 sin(2x) 4 sin(x) = 0 for all solutions 0 x < 2. x= Give your answers accurate to at least 2 decimal places and in a list separated by commas. #8 Points possible: 1. Total attempts: 3 Solve 2 cos2 (w) + 7 cos(w) + 5 = 0 for all solutions. w= where k Z #9 Points possible: 1. Total attempts: 3 Give the smallest two solutions of cos(2) = 0.4304 on [ 0, 2 ). Separate the two solutions with a comma. #10 Points possible: 1. Total attempts: 3 Solve 6 sin2 (x) + 5 cos(x) 7 = 0 for all solutions 0 x < 2 x= Give your answers accurate to 2 decimal places, as a list separated by commas Assignment 7.6 Modeling with Trigonometric Equations Name: Syd Hendricks #1 Points possible: 1. Total attempts: 3 Find a possible formula for the trigonometric function whose values are in the following table. x y 0 -1 2 -4 4 -7 6 -4 8 -1 10 -4 12 -7 y= #2 Points possible: 1. Total attempts: 3 A population of rabbits oscillates 20 above and below average during the year, hitting the lowest value in January (t = 0). The average population starts at 650 rabbits and increases by 200 each year. Find an equation for the population, P, in terms of the months since January, t. P (t) = #3 Points possible: 1. Total attempts: 3 A population of rabbits oscillates 22 above and below average during the year, hitting the lowest value in January (t = 0). The average population starts at 900 rabbits and increases by 9% each month. Find an equation for the population, P, in terms of the months since January, t. P (t) = #4 Points possible: 1. Total attempts: 3 A spring is attached to the ceiling and pulled 19 cm down from equilibrium and released. The amplitude decreases by 6% each second. The spring oscillates 14 times each second. Find an equation for the distance, D the end of the spring is below equilibrium in terms of seconds, t. D(t) = #5 Points possible: 1. Total attempts: 3 A spring is attached to the ceiling and pulled 14 cm down from equilibrium and released. After 4 seconds the amplitude has decreased to 12 cm. The spring oscillates 8 times each second. Assume that the amplitude is decreasing exponentially. Find an equation for the distance, D the end of the spring is below equilibrium in terms of seconds, t. D(t) = #6 Points possible: 1. Total attempts: 3 Find an equation of the form y = abx + c sin( x y 0 4 1 27 2 144 3 861 To fit the data: a= b= c= #7 Points possible: 1. Total attempts: 3 Match each graph with it's equation type: - (abx )sin(5x) - abx + sin(5x) - sin(5x) + mx + b - (mx + b)sin(5x) a. b. c. d. x) that fits the data below 2 #8 Points possible: 1. Total attempts: 3 The displacement of a mass suspended by a spring is modeled by the function h(t) = 15 sin(7t) Where h(t) is measured in centimeters, and t is measured in seconds Find the: Amplitude: Period: Frequency: cm seconds Hz #9 Points possible: 1. Total attempts: 3 Find a possible formula for the trigonometric function whose values are in the following table. x 0 4 8 12 16 20 24 y 3 1 3 5 3 1 3 Hint: Plot the points and sketch your own graph if needed. y= #10 Points possible: 1. Total attempts: 3 Find a possible formula for the trigonometric function whose values are in the following table. x y y= 0 8 3 4 6 0 9 4 12 8 15 4 18 0