Answered You can hire a professional tutor to get the answer.

QUESTION

NAME: _________________ M31 - Trig-Derivative Assignment

NAME: _________________M31 – Trig-Derivative Assignment (in Place of Unit Test) /71 1. Determine the exact value of each of the following expressions: (8 marks) a. cos 76 e. csc⁡(− b. tan 53 f. 2 sin2( 3 ) 4 g. cos2 (− ) c. sec 3 d. cot⁡(− 7)6 5)6 5 h. tan2 ( 6 ) 2. Determine all possible values of , 0 ≤ ≤ 2 , if (5 marks)1 a. cos = − 2 b. sin = √22 c. tan2 = 1 d. sec = √2 1 3. Simplify the following expressions: (4 marks)a. cos csc b. cos2 + tan2 cos 2 4. Prove the following equations are identities for all permissible values of . (4 marks)a. tan2 − sin2 = sin2 tan2 b. sin 1+cos + 1+cos sin = 2 csc 2 4 5. Verify the equation sin + cos tan = 2 sin numerically using = . (2 marks) 6. Evaluate the following limits. (6 marks)sin 2→0 a. lim sin 3→0 5 b. lim c. lim →0 4 tan 3 7. Differentiate the following trigonometric functions. Simplify where possible. (10 marks)a. () = √cot + 5 b. () = cos( 2 − 2)2 c. = sin2 () d. = cos 2(tan ) e. ℎ() = 3 csc cos3 f. = csc tan 4 8. Use implicit differentiation to find the derivative of the following relation, with respect to .Simplify the derivative as much as possible. a. sin + cos 2 = 2 (2 marks) b. + = cot( − ) (4 marks) 5 9. Find the derivative of the following functions. Simplify as much as possible.a. () = 5 (1 mark) b. = + − (1 mark) c. = sin( ) (1 mark) d. () = cos 2 (2 marks) e. = √⁡ (2 marks) f. 4 () = 2 +1 (2 marks) 6 10. Find the derivative of + = . State the solution in the form , where and ⁡contain onlypositive exponents. Simplify as much as possible. (3 marks) 11. Find the equation of the line tangent to the curve () = 2 at = 2 in general form.(3 marks) 7 12. Find the derivative of each of the following functions. Simplify as much as possible.a. () = ln( − 2) (1 mark) b. = ln 2 + ln 5 (1 mark) 1+ 2 c. () = ln (1− 3 ) (3 marks) 13. Find the equation of the line tangent to the curve () = ln at (1⁡, 0) in general form.(3 marks) 8 14. Find the equation of the line tangent to the curve () = sin 2cos at the point 4 , √2) (3 marks) 9

Show more
LEARN MORE EFFECTIVELY AND GET BETTER GRADES!
Ask a Question