Math / Trigonometry

QuestionEvaluate the function $f(x)=\tan ^{-1}(x)$ when $x=0$ . Give your answer in radians. 0 $\pi$ $\frac{3 \pi}{2}$ $2 \pi$

Studdy Solution

STEP 1

What is this asking? What's the arctangent of zero, or in other words, what angle has a tangent of zero?
And remember, we want the answer in radians! Watch out! Make sure your calculator is set to radian mode, and don't mix up tangent with arctangent!

STEP 2

1. Define the function
2. Evaluate at $x = 0$

STEP 3

We're given the function $f(x) = \tan^{-1}(x)$ .
This is the inverse tangent function, also known as arctangent.
It's asking: "What angle has a tangent of $x$ ?".

STEP 4

We want to find $f(0)$ , so we substitute $x = 0$ into our function: $f(0) = \tan^{-1}(0)$

STEP 5

Now, we're asking, "What angle has a tangent of zero?" Remember, the tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle.

STEP 6

Imagine that angle getting smaller and smaller.
As the angle approaches zero, the opposite side gets tiny, while the adjacent side stays put.
So the ratio gets closer and closer to zero.

STEP 7

Therefore, $\tan(0) = 0$ .
This means $\tan^{-1}(0) = 0$ .
So, $f(0) = \tan^{-1}(0) = 0$ .

STEP 8

Our final answer is $0$ radians!

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QuestionEvaluate the function $f(x)=\tan ^{-1}(x)$ when $x=0$ . Give your answer in radians. 0 $\pi$ $\frac{3 \pi}{2}$ $2 \pi$

Studdy Solution

STEP 1

What is this asking? What's the arctangent of zero, or in other words, what angle has a tangent of zero?
And remember, we want the answer in radians! Watch out! Make sure your calculator is set to radian mode, and don't mix up tangent with arctangent!

STEP 2

1. Define the function
2. Evaluate at $x = 0$

STEP 3

We're given the function $f(x) = \tan^{-1}(x)$ .
This is the inverse tangent function, also known as arctangent.
It's asking: "What angle has a tangent of $x$ ?".

STEP 4

We want to find $f(0)$ , so we substitute $x = 0$ into our function: $f(0) = \tan^{-1}(0)$

STEP 5

Now, we're asking, "What angle has a tangent of zero?" Remember, the tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle.

STEP 6

Imagine that angle getting smaller and smaller.
As the angle approaches zero, the opposite side gets tiny, while the adjacent side stays put.
So the ratio gets closer and closer to zero.

STEP 7

Therefore, $\tan(0) = 0$ .
This means $\tan^{-1}(0) = 0$ .
So, $f(0) = \tan^{-1}(0) = 0$ .

STEP 8

Our final answer is $0$ radians!

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QuestionEvaluate the function f(x)=tan⁡−1(x)f(x)=\tan ^{-1}(x)f(x)=tan−1(x) when x=0x=0x=0. Give your answer in radians. 0 π\piπ 3π2\frac{3 \pi}{2}23π​ 2π2 \pi2π

Studdy Solution

STEP 1

What is this asking? What's the *arctangent* of zero, or in other words, what angle has a tangent of zero?And remember, we want the answer in radians! Watch out! Make sure your calculator is set to radian mode, and don't mix up *tangent* with *arctangent*!

STEP 2

1. Define the function2. Evaluate at x=0x = 0x=0

STEP 3

We're given the function f(x)=tan⁡−1(x)f(x) = \tan^{-1}(x)f(x)=tan−1(x).This is the *inverse tangent* function, also known as *arctangent*.It's asking: "What angle has a tangent of xxx?".

STEP 4

We want to find f(0)f(0)f(0), so we **substitute** x=0x = 0x=0 into our function: f(0)=tan⁡−1(0)f(0) = \tan^{-1}(0)f(0)=tan−1(0)

STEP 5

Now, we're asking, "What angle has a tangent of **zero**?" Remember, the tangent of an angle is defined as the ratio of the *opposite side* to the *adjacent side* in a right-angled triangle.

STEP 6

Imagine that angle getting smaller and smaller.As the angle approaches zero, the opposite side gets tiny, while the adjacent side stays put.So the ratio gets closer and closer to zero.

STEP 7

Therefore, tan⁡(0)=0\tan(0) = 0tan(0)=0.This means tan⁡−1(0)=0\tan^{-1}(0) = 0tan−1(0)=0.So, f(0)=tan⁡−1(0)=0f(0) = \tan^{-1}(0) = 0f(0)=tan−1(0)=0.

STEP 8

Our **final answer** is 000 radians!

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionEvaluate the function $f(x)=\tan ^{-1}(x)$ when $x=0$ . Give your answer in radians. 0 $\pi$ $\frac{3 \pi}{2}$ $2 \pi$

What is this asking? What's the arctangent of zero, or in other words, what angle has a tangent of zero?
And remember, we want the answer in radians! Watch out! Make sure your calculator is set to radian mode, and don't mix up tangent with arctangent!

1. Define the function
2. Evaluate at $x = 0$

We're given the function $f(x) = \tan^{-1}(x)$ .
This is the inverse tangent function, also known as arctangent.
It's asking: "What angle has a tangent of $x$ ?".

We want to find $f(0)$ , so we substitute $x = 0$ into our function: $f(0) = \tan^{-1}(0)$

Now, we're asking, "What angle has a tangent of zero?" Remember, the tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle.

Imagine that angle getting smaller and smaller.
As the angle approaches zero, the opposite side gets tiny, while the adjacent side stays put.
So the ratio gets closer and closer to zero.

Therefore, $\tan(0) = 0$ .
This means $\tan^{-1}(0) = 0$ .
So, $f(0) = \tan^{-1}(0) = 0$ .

Our final answer is $0$ radians!