Calculus Questions

Test Chapter 8 Math 122 Form A Trigonometric Calculus too hard #16 and 8 and 15 Part I Trigonometry 1. Evaluate { approximate values to 4 decimal places } Show what you are putting into calculator A. csc(5.1) ________ B. cot(/3) ____________ 2. Simplify, without a fractional answer: 2 ¿ ¿ 3. a. Convert 225 to radians b. Convert 13/12 to degrees: approximate to 3 decimals ________ __________________ 2 2 4. If cos x = -2/3 and x is an angle with terminal side in Quadrant III , use the identity sin x +cos x=1 to find the sin(x) _____________________ tan(x) ______________________ 5. Sketch: y = 3sin(t ) Step one: {two cycles} What is the x-length of one cycle ___________ Step two: Break cycle into 5 x-coordinates and use a table of values to sketch 2 cycles Part II Derivatives Use the notes from the pretest or ones you have Part I. Differentiate 6. f ( x )=2sin ⁡(cot ( 2 x )) Type________ U = __________ U’ = ________ 7. f ( x )= √4 cos ⁡( x 3 ) Write answer in radical form. Hint : rewrite first Type________ U = __________ U’ = ________ 8.Find f’(x) f ( x )=x 3 sec ( x 3 ) You will need product rule… 2 9. f ( x )=tan(ecot ⁡(x ) ) 10. f ( x )=ln ( csc ( e−3 x ) ) Type________ U = __________ U’ = ________ Type________ U = __________ U’ = ________ Part III. Integration Use the notes you have made Indicate the model that you are using on the side of each problem Remember to show all work 11. ∫ 3 x cos ⁡(tan ¿ x ) sec (x )dx ¿ 2 2 12. ∫ 2 cos ( 4 x ) sin ( 4 x ) dx 2 13. ∫ t csc 2 2 Type________ U = __________ U’ = ________ Type________ U = __________ U’ = ________ 2 3t dt 2 Type________ U = __________ U’ = ________ 3 14. ∫ cot ¿ ¿ ¿ ¿ Type________ U = __________ U’ = ________ 2 Bonus (+.4) Use integration by parts to Evaluate: Step 1 Write out the formula ∫ xse c 2 ( x ) dx Step 2: Establish the parts U = _____________ du = ____________ dv = ____________ V = ______________________ Step 3: Plug in to formula and evaluate the second integral Part I Trigonometry 1. Evaluate { approximate values to 4 decimal places } a. tan2(-50°) _______ b. sec(5.1) ________ c. csc (/3) ____________ d. cot(46º) _______ 2 2. Simplify, without a fractional answer: Answer: csc(θ ) 3. Multiply and Simplify 1−cos x 3 sin x and leave answer in numerator only: ( secx−1 ) (secx+1) 4. a. Convert 315 to radians(in terms of ) b. Convert 11/12 to degrees: _______ approximate to 3 decimals ________ _______ 2 2 5. If sin x = -1/3 and x is an angle with terminal side in Quadrant III , use the identity sin x +cos x=1 to find the cos(x) _____________________ answer: cot(x) ______________________ 6. Sketch: y = 4cos(t) two cycles Part II Derivatives Use the Notes you have made Part I. Differentiate 7. f ( x )=4 sin ⁡(tan ( 2 x +1 )) Type _______ U =______ U’ = ______ 8. f ( x )= √3 cos x3 Hint : rewrite first Type _______ U =______ U’ = ______ 9. f ( x )=x 2 csc ( x 3 ) Type Product rule tanx 10. f ( x )=csc ⁡( e ) Type _______ U =______ U’ = ______ 11. f ( x )=2 xln ¿ Type Product rule 12. f ( x )=sin ⁡(ln ( sec ( e−2 x ) ) ) Type _______ U =______ U’ = ______ Part III. Integration Use the notes you have made Remember to show all work 13. ∫ 2 sin ( x 3 +1 ) x2 dx 14. ∫ 2 sin ( 3 x ) cos (3 x ) dx 2 Type _____________ U _____________ U’ ______________ Type _________________ U = _______________ U’__________ 3π 8 15. ∫ e csc ( 2 x ) csc ( 2 x ) cot ( 2 x ) dx Type _________________ U = _______________ U’__________ cos ⁡(2 x) dx 1+sin ⁡(2 x ) Type _________________ U = _______________ U’__________ 2t dt 3 Type _________________ U = _______________ U’__________ pi 8 16. ∫ 17. ∫ sec pi x 2 18. ∫ ∫ cos ( 2 y ) dy dx 0 0 19. Find the area under y=x 2 sec ( x 2 ) tan ⁡(x 2) from x = 0 to x = 1 {make sure to use radians} 20. 2 ∫ 1 3 tan ( √1x ) dx √x 3 Type _________________ U = _______________ U’__________