In these lessons, we will certainly look at just how to identify whether a Trigonometric role is Even, strange or Neither.

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Related PagesLessons ~ above TrigonometryInverse trigonometry Trigonometric features Even and also Odd Functions

What Is An also Function?

An even role is symmetric (by reflection) about the y-axis , i.e. F(-x) = f(x)

What Is an Odd Function?

An odd role is symmetric (by 180° rotation) about the origin, i.e. F(-x) = -f(x)

The adhering to table mirrors the also Trigonometric Functions and also Odd Trigonometric Functions. Scroll under the page for an ext examples and step by step solutions.


Even Trigonometric Functions and also Identities

Cosine function is even. Cos(-x) = cos x Secant duty is even. Sec(-x) = sec x

Odd Trigonometric Functions and also Identities

Sine duty is odd. Sin(-x) = - sin xCosecant function is odd. Csc(-x) = - csc xTangent duty is odd. Tan(-x) = - tan xCotangent duty is odd. Cot(-x) = - cot x

Determine whether A Trigonometric function Is Odd, Even, Or Neither

Examples v Trigonometric Functions: Even, strange or NeitherCosine function, Secant function, Sine function, Cosecant function, Tangent function, and also Cotangent function

instances With Trigonometric Functions: Even, strange Or Neither

Example 2

Determine even if it is the adhering to trigonometric role is Even, strange or Neithera) f(x) = sec x tan x

Example 3

b) g(x) = x4 sin x cos2x

Example 4

c) h(x) = cos x + sin x

how To use The Even-Odd properties Of The Trigonometric Functions?

Example: discover the specific value utilizing even-odd properties.(a) sin(-30°) (b) cos(-3π/4) (c) tan(-π/4)

just how To identify Trig duty Values Based Upon whether The function Is weird Or Even?

Determine each function value.If cos(x) = 0.5, climate cos(-x) = ___.If sin(x) = 0.15, then sin(-x) = ___.If tan(-x) = -3, then tan(x) = ___.If sec(-x) = 1.4, then sec(x) = ___.

exactly how To Use also Or Odd properties To evaluate Trig Functions?

Evaluate the trigonometric function by very first using even/odd nature to rewrite the expression through a optimistic angle. Give an exact answer do not use a calculator.sin(-45°)sec(210°)cos(-π6)csc(-3π/2)

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Shot the provided examples, or form in your own problem and also check her answer through the step-by-step explanations.