MATH 1-Assignment 3 - Unit 5.Knowledge/Understanding questions

MATH 1-Assignment 3 - Unit 5.Knowledge/Understanding questions Task 1: Knowledge/Understanding questions 1. 1.5/2 Determine the equivalent positive standard-position angle for each negative angle listed below. (2 marks: 1 mark each) a. −98∘ 360 °−98 °=262 ° b. −π 3 −π 3 × 180 π = −180 π 3π =−60° 360 °−60°=300 ° [This question was given in radians, so the answer should also be in radians.] 2. 3/4 Solve cotθ=1.6 for the domain 0≤θ≤360∘. Round your answer to the nearest degree. (4 marks: 1 mark for the correct value of tanθ; 1 mark for the correct related acute angle; and 1 mark each for the correct standard-position angles) cotθ=1.6 1 tanθ = 1 1.6 =0.625 tan −1 (0.625)=32 ° Standard-position angle for domain 0≤θ≤360 ° . Note: Related Acute Angle (RA) = 32° √ Quadrant 1: 0 °+32° = 32° Quadrant 2: 180° – 32° = 148 ° Quadrant 3: 180 °+32 °=¿ 212 ° Quadrant 4: 360 ° – 32°=328 ° [The tan ratio is only positive in quadrants 1 and 3; therefore, the angles are 32o and 212o only.] 3. 3/3 Use the unit circle to evaluate the following trigonometric ratios. Show your calculations. (3 marks: 1 mark each) a. sin90∘, x=0, y=1,r=1 sin 90 °= y r = 1 1 =1 b. cosπ, x=−1, y=0,r=1 cosπ= x r = −1 1 =−1 c. csc ( 3 π 2 ), x=0, y=−1,r=1 csc( 3π 2 )= 1 sinθ = r y = 1 −1 =−1 4. 2/2 Convert the following angles from degrees to radians. Leave your answers in exact form. (2 marks: 1 mark each) a. 220∘ 220 1 × π 180 = 11 π 9 radians b. 48∘ 48 1 × π 180 = 4 π 15 radians 5. 1.5/2 Convert the following angles from radians to degrees. Round your answers to the nearest degree. (2 marks: 1 mark each) a. 3 π 4 3 π 4 × 180 π = 3π ×180 4 π = 540 π 4 π 540 π 9 π =60° [ 540π 4 π =135°] b. 1.5 1.5× 180 π ¿ 270 π =86° √ 6. 1.5/2 Determine the related acute angle for 7 π 12 . In which quadrant does this angle lie? (2 marks) 7 π 12 × 180 π =105 ° Therefore the angle lies in quadrant II. 180 °−105 °=¿ 75 ° [This solution should be written in radians.] 7. 6/6 Determine the exact value for the following trigonometric ratios. (6 marks: 3 marks each) a. tan( 5 π