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mathematics UK Year 13 Mathematics (A Levels)

Solved problems for the chapter:

Cosecant, secant and cotangent ratios

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Compound angles formula

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1. Basic addition identities

2. Trigonometric functions of double angles

3. Trigonometric functions of half angles

4. Trigonometric functions of triple angles

4.1. Triple angle for sine

4.2. Triple angle of cosine

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Tangent and cotangent functions

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1. Graph of tangent and cotangent functions

1.1. Graph of tan x

1.2. The graph of cot x

2. Properties of the tangent and cotangent functions

2.1. The domain and range of values of tan x and cot x

2.1.1. The domain and range of values of tan x

2.1.2. The domain and range of values of cot x

2.2. The zeros of the functions of tan x and cot x

2.2.1. The zeros of tan x

2.2.2. The zeros of cot x

2.3. The discontinuous points of the tangent and cotangent functions

2.3.1. The discontinuous points of tan x

2.3.2. The discontinuous points of cot x

2.4. Determining if the tangent and cotangent functions are even or odd functions

2.4.1. For tan x

2.4.2. For cot x

2.5. The rising and falling of the tangent and cotangent functions

2.5.1. The rising of tan x

2.5.2. The falling cot x

2.6. Periodicity tan x in cot x

2.7. Continuity of tangent and cotangent functions

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Graph of tangent and cotangent functions

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1. Graphs of the form f (x) = A tan (x), g (x) = A cot (x)

2. Graphs of the form f (x) = tan (k x), g (x) = cot (k x)

2.1. Period of tangent and cotangent functions

3. Graphs of the form f (x) = tan (x) + n, f (x) = cot (x) + n

4. Graphs of the form f (x) = tan (x - a), g (x) = cot (x - a)

5. Graphs of the form f (x) = A tan (x - a) + n, g (x) = A cot (x - a) + n

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Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:cosecant%2C_secant_and_cotangent_ratios/5477/

Draw a graph of the function , .

Calculate the zeros of the function.
At what intervals is the function negative?

In the same coordinate system, draw the graph of the functions f and g.

and write down the abscissas of their intersections. Also specify the intervals at which .

Calculate the value of given that

Draw a graph of the function: