Function Properties of Trigonometric Functions

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These problems are about recognizing the properties that the trigonometric functions have as functions.

1 : Is $2\phi ^2$ a periodic function?

Yes No

2 : Is $\sec (\theta )$ a periodic function?

Yes No

2.1 : What is its period (in radians)? $\answer {2\pi }$

3 : Is $\tan (\gamma )$ a periodic function?

Yes No

3.1 : What is its period (in radians)? $\answer {\pi }$

4 : Is $\sin (\alpha )-9\alpha$ a periodic function?

Yes No

5 : Is $x-\sin (x)$ an even function, odd function, or neither?

Even Odd Neither

6 : Is $1+x\cos (x)$ an even function, odd function, or neither?

Even Odd Neither

6.1 : Decompose $1+x\cos (x)$ into even and odd functions.

Even part: $\answer {1}$
Odd part: $\answer {x\cos (x)}$

7 : Is $x^2+x^4-\cos (x)$ an even function, odd function, or neither?

Even Odd Neither

8 : Is $\sin ^2(y)-8y^4\sin (y)$ an even function, odd function, or neither?

Even Odd Neither

8.1 : Decompose $\sin ^2(y)-8y^4\sin (y)$ into even and odd functions.

Even part: $\answer {\sin ^2(y)}$
Odd part: $\answer {-8y^4\sin (y)}$