Bari Secondary School Trigonometry & Complex Number Assignment PDF

Assignment for Trigonometry and complex number PART ONE; MCQ, CIRCLE THE CORRECT ANSWER. 1. Express 150° into radian measure a) 4𝜋 5𝜋 b) 6 𝜋 c) 6 2𝜋 d) 5 2. Evaluate (4i)2 + 8 a) -8 b) 16 c) 8 d) -4 3. The angle 240° lies...

Assignment for Trigonometry and complex number PART ONE; MCQ, CIRCLE THE CORRECT ANSWER. 1. Express 150° into radian measure a) 4𝜋 5𝜋 b) 6 𝜋 c) 6 2𝜋 d) 5 2. Evaluate (4i)2 + 8 a) -8 b) 16 c) 8 d) -4 3. The angle 240° lies in a) First quadrant b) Third quadrant c) Fourth quadrant d) Second quadrant 4. The reference angle of 135° is a) 30° b) 60° c) 50° d) 45° 5. (3 + 2i) – (1 + 2i) is equal to a) 2 b) 2 – i c) 2 + 4i d) 3 – 4i 6. The hypotenuse of the triangle below is a). 15m c). 10m 8m b). 25m d).16m 7. Evaluate i16 6m a) -1 b) 1 c) 4 d) I 8. The value of negative angle sin (-30°) is 𝟏 𝟏 a) c) − 𝟐 𝟐 1 b) 4 d) 1 Page 1 of 6  9. 𝒄𝒐𝒔𝟐 𝜽 + 𝒔𝒊𝒏𝟐 𝜽 is equal to 𝟏 a) 1 c) 𝟐 b) 2 d) -1 10. Conjugate of (2 – 5i) is a) 2 – 5i b) 5i c) 5 + 2i d) 2 + 5i PART TWO: STRUCTURE QUESTIONS Q1. Find the value of six trigonometric functions of the acute angle triangle below a. Sin𝜃___________________________________ b. cos𝜃___________________________________ c. tan𝜃___________________________________ 4m d. cot𝜃___________________________________ e. csc𝜃___________________________________ f. sec𝜃___________________________________ 3m Question 2 A). Convert into Radians a). 90° b). 360° ………………………………………………………………………………………………… ………………………………………………………………………….. B). Convert into Degrees 𝜋 4𝜋 5𝜋 𝜋 a). 3 b). c). d). 4 3 6 ………………………………………………………………………………………………… ……………………………………………………………………………. QUESTION 3 A). Find the Reference angle 𝜃𝑟 for 𝜃 if a). 𝜃 = 60° : ……………………………………………………………… b). 𝜃 = 225° : ………………………………………………………………. c). 𝜃 = 315° : ………………………………………………………………. d). 𝜃 = 120° : ……………………………………………………………… Page 2 of 6 QUESTION 4 Prove the following identities a) tanθcot 2 θ=cotθ -------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------- ---------------------------------------------------------------- 2 2 b) cosθ + cosθ = 4secθ ------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------ c) cotθcscθsecθ=csc 2 θ ------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------ secθ d) =tanθ cscθ ---------------------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------------------- -------------------------------------------------- e) tan2θ + 1 = sec2θ -------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------- -------------------------------------------- f) cotx(cosx + tanx.sinx) = cscx -------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------- --------------------------------------------- Page 3 of 6 QUESTION 5 a) Sketch the graphs of the following functions. I. Y = Sinx for 0 ≤ x ≤ 360° II. Y = Cosx for 0 ≤ x ≤ 360° III. y = tanx for 0 ≤ x ≤ 360° IV. y = cotx for 0 ≤ x ≤ 360° V. y = secx for 0 ≤ x ≤ 360° VI. y = cscx for 0 ≤ x ≤ 360° 1 180° 360° 90° 𝟏𝟖𝟎° 270° 360° -1 1 1 90° 180° 270° 360° 90° 180° 270° 360° -1 -1 90° 180° 270° 360° 90° 180° 270° 360° Page 4 of 6  b) Find the exact value of the following A. Sin(-270°) B. Cos(45°) C. Sec180° D. Csc180° E. Cot60° F. Sec30° QUESTION 5 a) Add or Subtract the following complex numbers: A. (6 + 4i) + (-2 + i) 1 5𝑖 2 4𝑖 B. (3 + ) + (3 + ) 3 3 C. (2 + 3i) + (1 + i) – (3 + 2i) D. (8 + 4i) – (2 – 3i) b) If x = 2 + 2i, y = 4i, z = 4 + i. Find the: A. 2x -3y B. 4y +2z C. x + y - z c) Multiply or divide A. 4(3 – 2i) 1 B. (9 + 6𝑖) 3 C. (1 + 2𝑖)(1 − 4𝑖) D. (3i)(2 + 3i) Page 5 of 6  3−2𝑖 E. 1+𝑖 2+5𝑖 F. 3−2𝑖 d) Simplify the following A. I18 B. i28 C. √−196 D. √−72 e) If Z = 6 + 2i, Find: A. The conjugate of Z* B. Z + Z* C. Z Z* D. │Z│ Teacher: AhmedNur Ali Page 6 of 6