By sketching a suitable pair of graphs, show that the equation $$$\cot \frac{1}{2} x=1+\mathrm{e}^{-x}$$$ has exactly one root in the interval 0< x ≤ π. ....................................................................................................................................................... ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s21_qp_33 Year：2021 Question No：6(a)

Answer:

Sketch a relevant graph, e.g. $y=\cot \frac{1}{2} x$
Sketch a second relevant graph, e.g. $y=1+\mathrm{e}^{-x}$, and justify the given statement

Knowledge points:

3.2.2 understand the definition and properties of and ln x, including their relationship as inverse functions and their graphs (Including knowledge of the graph of for both positive and negative values of k.)

3.3.1 understand the relationship of the secant, cosecant and cotangent functions to cosine, sine and tangent, and use properties and graphs of all six trigonometric functions for angles of any magnitude

Answer:

Knowledge points:

Solution:

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