Find the value of an acute angle theta in degrees given cot(theta) = 1.
Check the final answer first, then review the worked steps.
Problem
Find the value of an acute angle theta in degrees given cot(theta) = 1.
Answer
\(45^{\circ}\)
Step-by-step solution
- Understand the problem: The problem asks us to find the value of an acute angle $\theta$ in degrees, given that $\cot(\theta) = 1$. An acute angle is an angle less than 90 degrees.
- Recall the definition of cotangent: The cotangent of an angle is the ratio of the adjacent side to the opposite side in a right-angled triangle, or alternatively, it is the reciprocal of the tangent: $\cot(\theta) = \frac{1}{\tan(\theta)}$.
- Relate cotangent to tangent: Since $\cot(\theta) = 1$, we can write $\frac{1}{\tan(\theta)} = 1$. This implies that $\tan(\theta) = 1$.
- Identify the angle for which tangent is 1: We need to find an angle $\theta$ such that $\tan(\theta) = 1$. We know that the tangent function has a value of 1 for specific angles. For acute angles, $\tan(45^{\circ}) = 1$.
- Verify the condition of being acute: The angle $45^{\circ}$ is indeed an acute angle because it is less than $90^{\circ}$.
- State the final answer: Therefore, the value of $\theta$ is $45^{\circ}$.