Determine the quadrant in which an angle, θ, lies if θ = 5.40 radians.
a. 4th quadrant
b. 3rd quadrant
c. 2nd quadrant
d. 1st quadrant
Answer is a.
To convert radian into degrees,
multiply the value of radian to 180/ Pi.
Therefore, 5.4 x 180/pi = 309.39, which is in the 4th quadrant.
same type of question as your last one
Well, let me put on my geometry hat and help you out. With an angle of 5.40 radians, we can see that it falls in the 4th quadrant. Just remember, it's all about the numbers, and in this case, the number points to the 4th quadrant like a GPS for angles. So, the answer is a. 4th quadrant.
To determine the quadrant in which an angle θ lies, we can use the following guidelines:
- In the first quadrant, both the x-coordinate and the y-coordinate of the point are positive.
- In the second quadrant, the x-coordinate is negative, while the y-coordinate is positive.
- In the third quadrant, both the x-coordinate and the y-coordinate are negative.
- In the fourth quadrant, the x-coordinate is positive, while the y-coordinate is negative.
Given that θ = 5.40 radians, we need to find the corresponding point on the unit circle.
To do this, we can convert θ into degrees by using the conversion factor: 180 degrees = π radians.
θ in degrees = 5.40 radians * (180 degrees / π radians) ≈ 309.69 degrees
We can see that 309.69 degrees lies in the fourth quadrant (where the angle is greater than 270 degrees and less than 360 degrees).
Therefore, the answer is:
a. 4th quadrant
To determine the quadrant in which an angle θ lies, we need to examine the sign of the trigonometric functions (sine and cosine) of the angle.
In this case, we can use the fact that an angle in standard position of 5.40 radians (or any angle larger than 2π) is equivalent to an angle of 5.40 - 2π radians.
Since 2π radians is one full revolution, subtracting 2π radians ensures that the angle remains within one full revolution.
Now, let's determine the signs of the sine and cosine of the angle.
To calculate the sine and cosine values, we can use the unit circle or a calculator:
sin(5.40 - 2π) ≈ -0.9915
cos(5.40 - 2π) ≈ 0.1294
From these values, we can conclude that the sine is negative and the cosine is positive.
In the coordinate plane, this means that the angle θ is in the fourth quadrant, where sine is negative and cosine is positive.
Therefore, the answer is:
a. 4th quadrant