Year 11 Extension 1 Trigonometry Assignment Date Due ...

Year 11 Extension 1 Trigonometry Assignment Date Due:Mathematics1. Find the value of x, giving your answer correct to two decimal places:(a)(b)x5 mx28°2. Find the value of θ correct to the nearest minute.67°14ʹ8.1 km7 mθ5 m3. If cos θ = 3 and 0° ≤ θ ≤ 360°, find: (a) sin θ5(b)cot θ4. Find the exact value of: (a) tan 225° (b) sin 135° (c) cos 300°5. Show that: (a) cosecθ – sinθ = cotθ cosθ(d) cos 240° (e) tan 480° (f) sin (45°)(b)tanθsecθ – 1 tanθsecθ + 1 = 2cotθ6. Solve 12cosθ = 7cosθ + 2 for 0° ≤ θ ≤ 360°.7. Find the value of x correct to one decimal place:(a)(b)x98°7 m4.7 m51°x56°11.3 m8. Find the area of the triangle drawn in Q7 (b).9. Point B is South-East of point A and at a distance of 2km from it.From point A, a point P bears 057°T and from B, point P bears 348°T.(a)(b)Find the size of ∠PAB and ∠APB.Find the distance from A to P, correct to two decimal places.

Extension 11. Prove that:sin A + B + sin(A – B)(a)cos A + B + cos(A – B) = tan A (b) sin2A + sinA1 + cos2A + cosA = tan A2. Find the exact value of cos105°.3. If α and β are acute angles and sin α = 3 5 and tan β = 7 , find the exact value of:24(a) sin(α – β) (b) tan(α + β) (c) cos2α4. If t = tan θ, express each of the following in terms of t.2(a) sin + cos (b)21 + cos5. Solve each of the following equations for 0° ≤ ≤ 360°:(a) cot – 3tan = 2 (b) sin2 = sin (c) sin 2 – 5sin – 2cos 2 = 06. (a) Write the expression 3sin – cos = 1 in the form R sin( – α)(b) Hence, or otherwise, solve the equation 3sin – cos = 1 for 0° ≤ ≤ 360°.7.BdC2000 m314°T 020°TA29°25°DEAn aeroplane flying at 200 m is observed to be on a bearing of 314°T with an angle of elevation of 29°.After 1 minute it is bearing 020°T at an angle of elevation of 25°. If it maintains this altitude, calculate:(a)(b)(c)(d)the distance AE to the nearest metrethe distance DE to the nearest metrethe size of angle AED to the nearest degreeand hence find the distance, d, the plant travels in that minute and its speed in km/h