Year 11 Extension 1 Trigonometry Assignment Date Due ...

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