Question

sketch the angle in standard position.

1. $35^circ$

a. image of coordinate system with angle
c. image of coordinate system with angle
b. image of coordinate system with angle
d. image of coordinate system with angle

1. find the radian measure of an angle of $110^circ$.

a. $\frac{11}{18\pi}$
b. $\frac{11\pi}{18}$
c. $\frac{18}{11\pi}$
d. $\frac{18\pi}{11}$

1. find the degree measure of an angle of $-\frac{\pi}{6}$ radians.

a. $-30\pi^circ$
b. $\frac{\pi}{1080}^circ$
c. $-30^circ$
d. $-0.52^circ$

Explanation:

Question 83

Step1: Recall standard position angle

An angle in standard position has its vertex at the origin and initial side along the positive x - axis. The measure of the angle is the amount of rotation from the initial side to the terminal side. For a positive angle like \(35^{\circ}\), we rotate counter - clockwise from the positive x - axis.

Step2: Analyze each option

• Option a: The angle is measured from the negative x - axis and is in the wrong direction (clockwise or related to negative x - axis), so it's incorrect.
• Option b: The angle is measured below the positive x - axis (in the fourth quadrant but the rotation direction is wrong as it should be counter - clockwise from positive x - axis for positive angle), so it's incorrect.
• Option c: The angle has its initial side on the positive x - axis and is rotated \(35^{\circ}\) counter - clockwise (which is correct for a positive \(35^{\circ}\) angle in standard position), so this is correct.
• Option d: The angle is measured from the negative x - axis and has a full - circle - like representation which is incorrect for a \(35^{\circ}\) angle.

Step1: Recall the conversion formula

To convert degrees to radians, we use the formula \( \text{radian measure}=\text{degree measure}\times\frac{\pi}{180}\).

Step2: Substitute the given degree measure

We are given a degree measure of \(110^{\circ}\). Substituting into the formula, we get \(110\times\frac{\pi}{180}=\frac{11\pi}{18}\).

Step1: Recall the conversion formula

To convert radians to degrees, we use the formula \( \text{degree measure}=\text{radian measure}\times\frac{180}{\pi}\).

Step2: Substitute the given radian measure

We are given a radian measure of \(-\frac{\pi}{6}\). Substituting into the formula, we get \(-\frac{\pi}{6}\times\frac{180}{\pi}\). The \(\pi\) terms cancel out, and \(\frac{180}{6} = 30\), so the degree measure is \(- 30^{\circ}\).

Answer:

c (the graph in option c)

Question 84