Trigonometric Functions And R Formula | Stanford University

University:
Stanford University
Course:
Introduction to Mathematical Thinking
Academic year:

2023
Views:

364

Pages:

3
Author:

MAlphen

Trigonometric Functions 3 1. Given that sin 𝐴 = − where 180° < 𝐴 < 270° and sin 𝐵 = 5 5 where 90° < 𝐵 < 180°, find 13 tan (𝐴 + 𝐵) without using a calculator. Ans: 16 63 Trigonometric Graph It is given that 𝑦 = 1 − 3 sin 2𝑥 for 𝜋 ≤ 𝑥 ≤ 𝜋. 2 (a) State the period of 𝑦. (b) Sketch the graph of 𝑦 = 1 − 3 sin 2𝑥. (c) By drawing a straight line on the same diagram as in part (ii), find the number of solutions 1 3 to the 3 sin 2𝑥 + 1 = 𝑥 for − 𝜋 ≤ 𝑥 ≤ 𝜋. 𝜋 2 equationAns: 2 R Formula The diagram shows a lawn made up of two triangles, 𝐴𝐵𝐶 and 𝐶𝐷𝐸. Triangle 𝐴𝐵𝐶 is an isosceles triangle where 𝐴𝐵 = 𝐴𝐶 = 6 m. 𝐷𝐸 = 7 m, 𝐴𝐸 = 3 m, and 𝐵𝐴 produced is perpendicular to 𝐷𝐸. Angle 𝐵𝐴𝐶 is 𝜃 and the area of the lawn is 𝑆 m2. (a) Show that 𝑆 = 18 sin 𝜃 + 31.5 cos 𝜃. (b) Hence, express 𝑆 as a single trigonometric term. (c) Given that 𝜃 can vary, find the maximum area of the lawn and the corresponding value of 𝜃.