University:
Ashworth College
Course:
C17S | College Mathematics
Academic year:

2023
Views:

110

Pages:

2
Author:

Jamiya Guerrero

Trigonometric Functions 1. (a) Show that 𝑥 ≠ 90𝑛° , 𝑛 ∈ ℤ 𝑐𝑜𝑠𝑒𝑐 2𝑥 + 𝑐𝑜𝑡 2𝑥 ≡ 𝑎 𝑐𝑜𝑡 𝑥 , where 𝑎 is constant to be found. (b) (5) Hence, or otherwise, solve, for 0 ≤ 𝜃 < 180° , 𝑐𝑜𝑠𝑒𝑐 (4𝜃 + 10° ) + 𝑐𝑜𝑡 (4𝜃 + 10° ) = √3 (Solutions based entirely on graphical or numerical methods are not acceptable.) 2. (a) (5) Prove that 1 + 𝑠𝑖𝑛 𝑥 𝑐𝑜𝑠 𝑥 + ≡ 2 𝑠𝑒𝑐 𝑥 1 + 𝑠𝑖𝑛 𝑥 𝑐𝑜𝑠 𝑥 𝑥 ≠ (2𝑛 + 1) 𝜋 2 (4) (b) Hence find, for 0 < 𝑥 < 2𝜋 , all the solutions of 1 + 𝑠𝑖𝑛 𝑥 𝑐𝑜𝑠 𝑥 + =4 1 + 𝑠𝑖𝑛 𝑥 𝑐𝑜𝑠 𝑥 giving your solutions in terms of π. (3) Question 1 a. b. Question 2 a. b.

Trigonometric Functions - Pure Math

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