Question

Write an expression describing all the angles that are coterminal with 1°. (Please use the variable k in your answer. Give your answer in degrees, but do not include a degree symbol in your answer.)

Answer 1

Answer: the expression is:

1 + k*360

where k is an integer number.

Step-by-step explanation:

First, the definition: Coterminal Angles share the same initial side and terminal sides. Then two angles A and B are coterminal if:

B = A + k*360°

Where k can be any integer number.

If we want to an expression that describes all the coterminal angles to 1°, we can write this as:

1° + k*360° with k integer.

Or

1 + k*360 (because you don't want the degree symbol in the answer)

Answer 2

The expression describing all the angles that are coterminal with 1° is $\theta' = 1^{\circ} + 180\cdot i$, $\forall \,i\, \in \mathbb{Z}$.

An angle is coterminal when it is in standard position and terminal sides are coincident, there two consecutive coterminal angles each 360°. Hence, we can describe all angles coterminal with the original one:

$\theta' = \theta + 180\cdot i$, $\forall \,i\, \in \mathbb{Z}$ (1)

Where:

• $\theta$ - Original angle, in sexagesimal degrees.
• $\theta'$ - Coterminal angle, in sexagesimal degrees.
• $i$ - Index.

If we know that $\theta = 1^{\circ}$, then the set of all angles that are coterminal is represented by this expression:

$\theta' = 1^{\circ} + 180\cdot i$

The expression describing all the angles that are coterminal with 1° is $\theta' = 1^{\circ} + 180\cdot i$, $\forall \,i\, \in \mathbb{Z}$.

We kindly invite to check this question on coterminal angles: https://brainly.com/question/23093580