3) sin 265 cos 25 - cos 265 sin 25 C) Find the exact value by using a sum or difference identity. 4) sin 165 C) - 627

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1 Bonus Assignment Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the given information to find the exact value of the expression. 1) sin =, lies in quadrant II, and cos =, lies in quadrant I Find cos ( - ). 1) Find the exact value of the expression. ) cos 1 - ) ) sin cos - cos sin ) Find the exact value by using a sum or difference identity. ) sin 1 ) - ( - 1) - ( + 1) ( - 1) ( + 1) Find the exact value under the given conditions. ) sin =, 0 < < 0 ; cos = 9, 0 < < Find tan ( + ). ) Describe the graph using another equation. ) y = cos x + - cos x - ) -sin x -sin x -cos x -cos x 1

2 Find the exact value by using a difference identity. 7) tan 8 7) Identify and in the following expression which is the right side of the formula for cos ( - ). 8) cos (1 ) cos ( ) + sin (1 ) sin ( ) 8) = -, = 1 = 1, = =, = 1 = -1, = Use the given information to find the exact value of the expression. 9) sin =, lies in quadrant II, and cos =, lies in quadrant I Find cos ( - ). 9) Find the exact value by using a sum or difference identity. 10) sin (1-9 ) 10) ) If a projectile is fired at an angle and initial velocity v, then the horizontal distance traveled by the 11) projectile is given by D = 1 1 v sin cos. Express D as a function of. D = 1 8 v sin D = 1 1 v cos D = 1 v sin D = 1 1 v sin Complete the identity. 1) sin x - cot x =? 1) -cot x cos x cot x cos x -tan x cos x cot x cos x Rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1. 1) 8 cos x 1) + cos x 1 cos x 1 + cos x - cos x Use the given information to find the exact value of the trigonometric function. 1) cos = -, sin > 0 Find cos. 1)

3 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Verify the identity. 1) sint = sint cost 1) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) An airplane flying faster than the speed of sound creates sound waves that form a cone. If is the 1) vertex angle of the cone and m is the Mach number for the speed of the plane, then sin = 1 m (m > 1). Find the Mach number to the nearest tenth if = Use the given information to find the exact value of the trigonometric function. 17) sec =, lies in quadrant I Find cos. 17) Write the expression as the sine, cosine, or tangent of a double angle. Then find the exact value of the expression. 18) sin 10 cos 10 18) Use the given information to find the exact value of the expression. 19) tan = 1, lies in quadrant III Find sin. 19) Use the given information to find the exact value of the trigonometric function. 0) sin = - 0 9, lies in quadrant IV Find cos. 0) Express the product as a sum or difference. 1) sin 8x cos x 1) 1 (sin 1x + cos x) sin (cos x ) 1 (cos 1x - cos x) 1 (sin 1x + sin x)

4 ) cos x cos x ) 1 (cos x + cos 9x) cos 0x 1 (cos 9x - cos x) 1 (cos 9x - sin x) Complete the identity. ) sin x (sin x + sin 7x) =? ) 1 cos x (cos x + cos 7x) 1 cos x (cos x - cos 7x) cos x (cos x + cos 7x) cos x (cos x - cos 7x) Express the sum or difference as a product. ) sin 7 + sin 1 ) - Show that the equation is not an identity by finding a value of x for which both sides are defined but not equal. ) sin x + sin 7x = sin 11x ) 0 ) The sound produced by touching each button on a touch-tone phone is described by ) y = sin lt + sin ht where l and h are the low and high frequencies (cycles per second) in the figure shown. Use a calculator to find the graph of the sound emitted by touching the key in a [0, 0.01, 0.001] by [-,, 1] viewing rectangle.

5 Express the product as a sum or difference. 7) sin x cos x 7) 1 (sin 11x - sin x) 1 (cos 11x - cos x) sin (cos 0x) 1 (cos 11x + sin x) Fill in the blank using the word product, sum, quotient, or difference ) The formula cos - cos = - sin sin can be used to change a of two cosines into the of two sine expressions. 8) sum, quotient difference, quotient sum, product difference, product Complete the identity. sin x + sin 11x 9) cos x + cos 11x =? 9) tan x + tan 11x tan 8x tan x tan 8x tan 8x cot x

6 0) sin x + sin y cos x + cos y =? 0) tan x + tan y cot x - y tan x - y tan x + y Solve the equation on the interval [0, ). 1) sin x + sin x = 0 1) 0,,, 0,, 0,,, 0,,, Find all solutions of the equation. ) tan x sec x = - tan x ) x = + n or x = + n or x = n x = + n or x = + n or x = n x = + n or x = + n or x = n x = + n or x = + n or x = n Solve the equation on the interval [0, ). ) sin x - cos x = 0 ),,,,, 7 Use substitution to determine whether the given x-value is a solution of the equation. ) sin x = -, x = - ) Yes No Solve the equation on the interval [0, ). ) cos x + + cos x - = 1 ),, 0, Find all solutions of the equation. ) sin x - = 0 ) x = + n or x = + n x = + n or x = + n x = + n or x = + n x = + n or x = + n

7 7) The weekly sales in thousands of items of a product has a seasonal sales record approximated by 7) n = sin t (t is time in weeks with t = 1 referring to the first week in the year). During which week(s) will the sales equal 9,990 items? week, week 0, and week week 0 and week 7 week 1 and week 0 week and week 7 Solve the equation on the interval [0, ). 8) tan x sin x = tan x 8),, 0, 0, Solve the equation on the interval [0, ). 9) cos x + cos x + 1 = 0 9), 7, 0) A generator produces an alternating current according to the equation I = 8 sin 1 t, where t is 0) time in seconds and I is the current in amperes. What is the smallest time t such that I =? 1 88 second 1 second 1 second 1 7 second 7