Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Algebra 3 / Trigonometry Midterm Review Packet Name: __________________ Date: ___________ Pd: ___ Find the positive and negative coterminal angle. 1.) 150 2.) pos: _____ neg: _____ 2 3 3.) pos: _____ neg: _____ 50 pos: _____ neg: _____ Convert to Decimal Degree: 4.) 12345'17" = _________ 5.) 10135'10" = ___________ Convert to DMS: 6.) 23.4576 = __________ 7.) 103.6754 = ___________ Change from degrees to radians: 8.) 105 = _______ 9.) 135 = ________ 10.) 50 = ________ Change from radians to degrees: 11.) 3 = _______ 4 12.) 7 = _________ 6 13.) 11 = ________ 4 Find the length of the arc given: 14.) 4 and r = 16 inches 15.) 110 and r = 3 meters Algebra 3 / Trigonometry Midterm Review Packet Name: __________________ Date: ___________ Pd: ___ Find the values of the six trig functions: 16.) sin _____ csc _____ cos _____ sec _____ tan _____ cot _____ 7 18.) x 4 21 16 X = ________ 19.) = _________ 20.) 14 18 5 x 24 X = ________ 12 5 Set up a trig equation, then solve for the indicated value. 17.) 13 = __________ Algebra 3 / Trigonometry Midterm Review Packet Name: __________________ Date: ___________ Pd: ___ Use your calculator to find the indicated values. 21.) sin 57 = ______ 22.) cos 12340’ = ______ 23.) cot 100 = ______ 24.) csc 214.73 = _______ 25.) sec = -1.46; = _________ 26.) sin = .9376; = _________ 27.) csc = .4819; = _________ Given sin = 5 and is in quadrant III, find: 13 28.) sin _____ csc _____ cos _____ sec _____ tan _____ cot _____ 29.) A man standing 12 ft from the base of a tree has an angle of elevation to the top of the tree of 33. Find the height of the tree. 30.) A 96-foot tree casts a shadow that is 120 feet long. What is the angle of elevation of the sun? 31.) From the top of a 200 foot lighthouse, the angle of depression to a ship in the ocean is 23. How far is the ship from the base of the lighthouse? Algebra 3 / Trigonometry Midterm Review Packet Name: __________________ Date: ___________ Pd: ___ Find the reference angle, and then determine the value of the function. 32.) sin 210 Reference Angle ____________ Value ____ 33.) cos 300 ____________ ____ 34.) tan 150 ____________ ____ 35.) sec 225 ____________ ____ 36.) csc 315 ____________ ____ In which quadrant do the following conditions hold true? 37.) sin > 0 and cos < 0 ______ 38.) cos > 0 and tan < 0 ______ Identify the amplitude, period, phase shift and vertical shift for each of the following. 39.) y = 2 cos (4 - ) 40.) y = 5 1 sin 2 1 41.) y = 1 - sin ( ) 2 2 Amp: __________ Period: __________ Phase Shift: ________ Vertical Shift: _________ Amp: __________ Period: __________ Phase Shift: ________ Vertical Shift: _________ Amp: __________ Period: __________ Phase Shift: ________ Vertical Shift: _________ Algebra 3 / Trigonometry Midterm Review Packet 3 42.) y = -3 cos (3x + ) 2 Name: __________________ Date: ___________ Pd: ___ Amp: __________ Period: __________ Phase Shift: ________ Vertical Shift: _________ Graph the following: 4 3 43.) y = cos ( + ) 2 1 - 2 - 3 2 - - 2 -1 3 2 2 5 2 2 4 7 2 3 -2 -3 -4 4 1 44.) y = 2 sin ( x ) 2 2 3 2 1 - 2 - 3 2 - - 2 -1 3 2 2 2 5 2 3 7 2 4 -2 -3 4 -4 45.) y = sec (x - ) 3 2 1 - 2 - 3 2 - - 2 -1 3 2 2 5 2 2 4 7 2 3 -2 -3 -4 4 46.) y = 2 csc x 3 2 1 - 2 - 3 2 - - 2 -1 -2 -3 -4 2 3 2 2 5 2 3 7 2 4 Algebra 3 / Trigonometry Midterm Review Packet Name: __________________ Date: ___________ Pd: ___ 4 47.) y = tan x 3 2 1 - 2 - 3 2 - - 2 -1 3 2 2 2 5 2 3 7 2 4 -2 -3 -4 4 3 48.) y = cot x 2 1 - 2 - 3 2 - - 2 -1 2 3 2 2 5 2 3 -2 -3 -4 Find the values using the unit circle: 49.) arcsin ( 3 ) = ________ 2 51.) arccos ( 2 ) = _________ 2 50.) sin 1 (1) = ___________ 52.) tan 1 ( 3) = ___________ Find the value of the composition function: 53.) sin(arccos 3 ) = ________ 2 1 54.) tan(arcsin( )) = ________ 2 Simplify using the trig identities: 55.) tan = ________ sin 56.) cos2 x sin2 x = _________ 2 7 2 4 Algebra 3 / Trigonometry Midterm Review Packet Name: __________________ Date: ___________ Pd: ___ Find the solutions to the given equations over the interval [0, 2 ). 57.) 2 cos x + 1 = 0 58.) 2 sin2 x = 1 59.) 3tan3 x tan x 0 Use the Law of Sines or the Law of Cosines to solve: A 60.) x = __________ 80° 12 70° B C x A 61.) = __________ 60° 9 B C 15 62.) x = __________ A x 7 63° B 23 C Algebra 3 / Trigonometry Midterm Review Packet Name: __________________ Date: ___________ Pd: ___ A 63.) = __________ 14 8 B C 10 64.) From point A on the ground, the angle of elevation to the top of a tall building is 24. From point B, which is 600 ft closer to the building, the angle of elevation is measured to be 30. Find the height of the building. Building 24° A 30° B Ground Find the area of the following triangles: A 65.) A 66.) 34° B B C 5 Area = _________ 14 6 8 Area = __________ C A 68.) 5 B 17 Area = ___________ A 67.) 12 7 7 C B 35° 8 Area = ____________ C Algebra 3 / Trigonometry Midterm Review Packet Name: __________________ Date: ___________ Pd: ___ Use a sum or difference formula to find the exact value of the following: 69.) tan 285 70.) sin 345 71.) cos 195 72.) cos( ) if cos 7 , 25 73. sin( ) if cos 3 , 5 3 5 3 < < 2 and sin , < < 2 13 2 8 < < and cos , 0< < 17 2 2