Trigonometric Functions - Math

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Question

Simplify the function below:

$f(x)=cos^2(\frac{1}{2}cos^{-1}x)$

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Answer

We need to use the following formulas:

a) $cos^2x=\frac{1+cos2x}{2}$

and

b) $cos(cos^{-1}x)=x$

We can simplify as follows:

$f(x)=cos^2(\frac{1}{2}cos^{-1}x)=\frac{1+cos(cos^{-1}x)}{2}=\frac{1+x}{2}$

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Question

Which of the following is not in the range of the function $y = \sin{x}$ ?

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Answer

The range of the function $y= \sin x$ is all numbers between and (the sine wave never goes above or below this).

Of the choices given, $\frac{3}{2}$ is greater than and thus not in this range.

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Question

Simplify the function below:

$f(x)=cos^2(\frac{1}{2}cos^{-1}x)$

Tap to reveal answer

Answer

We need to use the following formulas:

a) $cos^2x=\frac{1+cos2x}{2}$

and

b) $cos(cos^{-1}x)=x$

We can simplify as follows:

$f(x)=cos^2(\frac{1}{2}cos^{-1}x)=\frac{1+cos(cos^{-1}x)}{2}=\frac{1+x}{2}$

← Didn't Know|Knew It →

Question

Which of the following is not in the range of the function $y = \sin{x}$ ?

Tap to reveal answer

Answer

The range of the function $y= \sin x$ is all numbers between and (the sine wave never goes above or below this).

Of the choices given, $\frac{3}{2}$ is greater than and thus not in this range.

← Didn't Know|Knew It →

Question

Simplify the function below:

$f(x)=cos^2(\frac{1}{2}cos^{-1}x)$

Tap to reveal answer

Answer

We need to use the following formulas:

a) $cos^2x=\frac{1+cos2x}{2}$

and

b) $cos(cos^{-1}x)=x$

We can simplify as follows:

$f(x)=cos^2(\frac{1}{2}cos^{-1}x)=\frac{1+cos(cos^{-1}x)}{2}=\frac{1+x}{2}$

← Didn't Know|Knew It →

Question

Which of the following is not in the range of the function $y = \sin{x}$ ?

Tap to reveal answer

Answer

The range of the function $y= \sin x$ is all numbers between and (the sine wave never goes above or below this).

Of the choices given, $\frac{3}{2}$ is greater than and thus not in this range.

← Didn't Know|Knew It →

Question

Simplify the function below:

$f(x)=cos^2(\frac{1}{2}cos^{-1}x)$

Tap to reveal answer

Answer

We need to use the following formulas:

a) $cos^2x=\frac{1+cos2x}{2}$

and

b) $cos(cos^{-1}x)=x$

We can simplify as follows:

$f(x)=cos^2(\frac{1}{2}cos^{-1}x)=\frac{1+cos(cos^{-1}x)}{2}=\frac{1+x}{2}$

← Didn't Know|Knew It →

Question

Which of the following is not in the range of the function $y = \sin{x}$ ?

Tap to reveal answer

Answer

The range of the function $y= \sin x$ is all numbers between and (the sine wave never goes above or below this).

Of the choices given, $\frac{3}{2}$ is greater than and thus not in this range.

← Didn't Know|Knew It →

Knew It

Trigonometric Functions - Math

Simplify the function below:

We need to use the following formulas: a) and b) We can simplify as follows:

Which of the following is not in the range of the function ?

The range of the function is all numbers between and (the sine wave never goes above or below this). Of the choices given, is greater than and thus not in this range.

Simplify the function below:

We need to use the following formulas: a) and b) We can simplify as follows:

Which of the following is not in the range of the function ?

The range of the function is all numbers between and (the sine wave never goes above or below this). Of the choices given, is greater than and thus not in this range.

Simplify the function below:

We need to use the following formulas: a) and b) We can simplify as follows:

Which of the following is not in the range of the function ?

The range of the function is all numbers between and (the sine wave never goes above or below this). Of the choices given, is greater than and thus not in this range.

Simplify the function below:

We need to use the following formulas: a) and b) We can simplify as follows:

Which of the following is not in the range of the function ?

The range of the function is all numbers between and (the sine wave never goes above or below this). Of the choices given, is greater than and thus not in this range.

Simplify the function below:

$f(x)=cos^2(\frac{1}{2}cos^{-1}x)$

We need to use the following formulas:

a) $cos^2x=\frac{1+cos2x}{2}$

and

b) $cos(cos^{-1}x)=x$

We can simplify as follows:

$f(x)=cos^2(\frac{1}{2}cos^{-1}x)=\frac{1+cos(cos^{-1}x)}{2}=\frac{1+x}{2}$

Which of the following is not in the range of the function $y = \sin{x}$ ?

The range of the function $y= \sin x$ is all numbers between and (the sine wave never goes above or below this).

Of the choices given, $\frac{3}{2}$ is greater than and thus not in this range.

Simplify the function below:

$f(x)=cos^2(\frac{1}{2}cos^{-1}x)$

We need to use the following formulas:

a) $cos^2x=\frac{1+cos2x}{2}$

and

b) $cos(cos^{-1}x)=x$

We can simplify as follows:

$f(x)=cos^2(\frac{1}{2}cos^{-1}x)=\frac{1+cos(cos^{-1}x)}{2}=\frac{1+x}{2}$

Which of the following is not in the range of the function $y = \sin{x}$ ?

The range of the function $y= \sin x$ is all numbers between and (the sine wave never goes above or below this).

Of the choices given, $\frac{3}{2}$ is greater than and thus not in this range.

Simplify the function below:

$f(x)=cos^2(\frac{1}{2}cos^{-1}x)$

We need to use the following formulas:

a) $cos^2x=\frac{1+cos2x}{2}$

and

b) $cos(cos^{-1}x)=x$

We can simplify as follows:

$f(x)=cos^2(\frac{1}{2}cos^{-1}x)=\frac{1+cos(cos^{-1}x)}{2}=\frac{1+x}{2}$

Which of the following is not in the range of the function $y = \sin{x}$ ?

The range of the function $y= \sin x$ is all numbers between and (the sine wave never goes above or below this).

Of the choices given, $\frac{3}{2}$ is greater than and thus not in this range.

Simplify the function below:

$f(x)=cos^2(\frac{1}{2}cos^{-1}x)$

We need to use the following formulas:

a) $cos^2x=\frac{1+cos2x}{2}$

and

b) $cos(cos^{-1}x)=x$

We can simplify as follows:

$f(x)=cos^2(\frac{1}{2}cos^{-1}x)=\frac{1+cos(cos^{-1}x)}{2}=\frac{1+x}{2}$

Which of the following is not in the range of the function $y = \sin{x}$ ?

The range of the function $y= \sin x$ is all numbers between and (the sine wave never goes above or below this).

Of the choices given, $\frac{3}{2}$ is greater than and thus not in this range.