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

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Related PagesLessons on TrigonometryInverse trigonometry Trigonometric functions Even and also Odd Functions

What Is An even Function?

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

What Is one Odd Function?

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

The adhering to table reflects the also Trigonometric Functions and Odd Trigonometric Functions. Scroll down the page for more examples and step by action solutions.


Even Trigonometric Functions and Identities

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

Odd Trigonometric Functions and Identities

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

Determine even if it is A Trigonometric role Is Odd, Even, Or Neither

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

examples With Trigonometric Functions: Even, odd Or Neither

Example 2

Determine whether the complying with trigonometric function is Even, weird 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

just how To usage The Even-Odd properties Of The Trigonometric Functions?

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

exactly how To determine Trig function 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, climate sin(-x) = ___.If tan(-x) = -3, climate tan(x) = ___.If sec(-x) = 1.4, climate sec(x) = ___.

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

Evaluate the trigonometric role by first using even/odd nature to rewrite the expression v a confident angle. Give an exact answer carry out not use a calculator.sin(-45°)sec(210°)cos(-π6)csc(-3π/2)

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