Question

Which functions are symmetric with respect to the origin?

y = arcsinx and y = arccosx
y = arccosx and y = arctanx
y = arctanx and y = arccotx
y = arcsinx and y = arctanx

Answer 1

Answer:

The correct option is;

y = arcsinx and y = arctanx

Step-by-step explanation:

The given options are;

1) y = arcsinx and y = arccosx

Here, we have at the origin, where x = 0,  arccosx ≈ 1.57 while arcsinx = 0

Therefore arccosx does not intersect arcsinx at the origin for it to be symmetrical to arcsinx or the origin

2)  y = arccosxy and y = arctanx

Here arctanx = 0 when x = 0 and arcos x = 1.57 when x = 0 therefore, they are not symmetrical

3) y = arctanx and y = arccotx

Similarly, At x = 0, arccotx = 1.57 therefore, they are not symmetrical

4) y = arcsinx and y = arctanx

Both functions arcsinx and arctanx pass through the origin and their shapes are similar but inverted as they go from negative to positive.

Answer 2

The function are symmetric with respect to the origin is y = arcsinx and y = arctanx and this can be determined by using the trigonometric property.

The following steps can be used in order to determine which functions are symmetric with respect to the origin:

Step 1 - Check all the options given in order to determine which functions are symmetric with respect to the origin.

Step 2 - Substitute (x = 0) in option a), that is:

$\rm y = sin^{-1}(0)=0$

$\rm y = cos^{-1}(0)=1.57$

Step 3 - Substitute (x = 0) in option b), that is:

$\rm y = cos^{-1}(0)=1.57$

$\rm y = tan^{-1}(0)=0$

Step 4 - Substitute (x = 0) in option c), that is:

$\rm y = tan^{-1}(0)=0$

$\rm y = cot^{-1}(0)=1.57$

Step 5 - Substitute (x = 0) in option d), that is:

$\rm y = tan^{-1}(0)=0$

$\rm y = sin^{-1}(0)=0$

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https://brainly.com/question/13710437