QuestionCalculate the value of $\cos 90^{\circ} + \cot 45^{\circ}$ without using a calculator.

Studdy Solution

STEP 1

Assumptions1. We are working with degrees, not radians. . We are asked to find the exact value of the expression, so we will not use a calculator.
3. We know the exact values of cosine and cotangent for the given angles from the unit circle and the definition of cotangent.

STEP 2

The expression we are trying to simplify is $\cos90^{\circ}+\cot45^{\circ}$

STEP 3

We know from the unit circle that the cosine of90 degrees is0. So we replace $\cos90^{\circ}$ with0 in our expression.
$0+\cot45^{\circ}$

STEP 4

The cotangent of an angle is defined as the reciprocal of the tangent of that angle. We know from the unit circle that the tangent of45 degrees is1, so the cotangent of45 degrees is also1. So we replace $\cot45^{\circ}$ with1 in our expression.
$0+1$

STEP 5

Finally, we simplify the expression by adding the numbers.
$0+1 =1$ So, the exact value of the expression $\cos90^{\circ}+\cot45^{\circ}$ is1.

Was this helpful?

QuestionCalculate the value of $\cos 90^{\circ} + \cot 45^{\circ}$ without using a calculator.

Studdy Solution

STEP 1

Assumptions1. We are working with degrees, not radians. . We are asked to find the exact value of the expression, so we will not use a calculator.
3. We know the exact values of cosine and cotangent for the given angles from the unit circle and the definition of cotangent.

STEP 2

The expression we are trying to simplify is $\cos90^{\circ}+\cot45^{\circ}$

STEP 3

We know from the unit circle that the cosine of90 degrees is0. So we replace $\cos90^{\circ}$ with0 in our expression.
$0+\cot45^{\circ}$

STEP 4

The cotangent of an angle is defined as the reciprocal of the tangent of that angle. We know from the unit circle that the tangent of45 degrees is1, so the cotangent of45 degrees is also1. So we replace $\cot45^{\circ}$ with1 in our expression.
$0+1$

STEP 5

Finally, we simplify the expression by adding the numbers.
$0+1 =1$ So, the exact value of the expression $\cos90^{\circ}+\cot45^{\circ}$ is1.

Get Studdy

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.

QuestionCalculate the value of cos⁡90∘+cot⁡45∘\cos 90^{\circ} + \cot 45^{\circ}cos90∘+cot45∘ without using a calculator.

Studdy Solution

STEP 1

Assumptions1. We are working with degrees, not radians. . We are asked to find the exact value of the expression, so we will not use a calculator.3. We know the exact values of cosine and cotangent for the given angles from the unit circle and the definition of cotangent.

STEP 2

The expression we are trying to simplify iscos⁡90∘+cot⁡45∘\cos90^{\circ}+\cot45^{\circ} cos90∘+cot45∘

STEP 3

We know from the unit circle that the cosine of90 degrees is0. So we replace cos⁡90∘\cos90^{\circ}cos90∘ with0 in our expression.0+cot⁡45∘0+\cot45^{\circ} 0+cot45∘

STEP 4

The cotangent of an angle is defined as the reciprocal of the tangent of that angle. We know from the unit circle that the tangent of45 degrees is1, so the cotangent of45 degrees is also1. So we replace cot⁡45∘\cot45^{\circ}cot45∘ with1 in our expression.0+10+10+1

STEP 5

Finally, we simplify the expression by adding the numbers.0+1=10+1 =10+1=1So, the exact value of the expression cos⁡90∘+cot⁡45∘\cos90^{\circ}+\cot45^{\circ}cos90∘+cot45∘ is1.

Get Studdy

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.

QuestionCalculate the value of $\cos 90^{\circ} + \cot 45^{\circ}$ without using a calculator.

Assumptions1. We are working with degrees, not radians. . We are asked to find the exact value of the expression, so we will not use a calculator.
3. We know the exact values of cosine and cotangent for the given angles from the unit circle and the definition of cotangent.

The expression we are trying to simplify is $\cos90^{\circ}+\cot45^{\circ}$

We know from the unit circle that the cosine of90 degrees is0. So we replace $\cos90^{\circ}$ with0 in our expression.
$0+\cot45^{\circ}$

The cotangent of an angle is defined as the reciprocal of the tangent of that angle. We know from the unit circle that the tangent of45 degrees is1, so the cotangent of45 degrees is also1. So we replace $\cot45^{\circ}$ with1 in our expression.
$0+1$

Finally, we simplify the expression by adding the numbers.
$0+1 =1$ So, the exact value of the expression $\cos90^{\circ}+\cot45^{\circ}$ is1.