Which angle has a larger cosine value?

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In summary, the problem involves comparing the values of two cosine expressions: cos (B - π/2) and cos (θ + π/2). The textbook states that the correct answer is cos (B - π/2) > cos (θ + π/2), while the student found the opposite. Upon further review, it appears that the values given in the problem may have been incorrect, as the textbook and the student's calculations used different input values for cos B and cos θ. Additionally, the problem statement did not specify which quadrant(s) the angles B and θ terminate in. Further clarification is needed to determine the correct answer.
  • #1
mathdad
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We are given the following:

Let B = beta

cos B = cos (2_/6)/5

cos θ = cos 3/4

Which angle is larger:

cos (B - π/2) or cos (θ + π/2)?

I found cos (B - π/2) to be about 0.557.

I found cos (θ + π/2 to be about 0.731.

So, 0.731 > 0.557.

My answer is cos (θ + π/2) > cos (B - π/2).

Book's answer is cos (B - π/2) > cos (θ + π/2).

Why is my answer wrong?
 
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  • #2
what is this value supposed to be?

(2_/6)/5
 
  • #3
skeeter said:
what is this value supposed to be?

See picture.

View attachment 7938
 

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  • #4
recheck the problem ... are you sure it's not

$\cos{\beta} = \dfrac{2\sqrt{6}}{5}$ and $\cos{\theta} = \dfrac{3}{4}$

instead of

$\cos{\beta} = \cos\left(\dfrac{2\sqrt{6}}{5}\right)$ and $\cos{\theta} = \cos\left(\dfrac{3}{4}\right)$

?
 
  • #5
Yes, you are right. So, why is the textbook right? Why is my answer wrong?
 
  • #6
RTCNTC said:
Yes, you are right. So, why is the textbook right? Why is my answer wrong?

one more note regarding the problem statement ...

Which angle is larger:

cos (B - π/2) or cos (θ + π/2)?

$\cos\left(\beta - \dfrac{\pi}{2}\right)$ and $\cos\left(\theta + \dfrac{\pi}{2}\right)$ are not angle values ... maybe which value of cosine is larger?

one more question, does the problem statement say anything about which quadrant(s) $\beta$ and $\theta$ terminate?
 
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  • #7
skeeter said:
one more note regarding the problem statement ...
$\cos\left(\beta - \dfrac{\pi}{2}\right)$ and $\cos\left(\theta + \dfrac{\pi}{2}\right)$ are not angle values ... maybe which value of cosine is larger?

one more question, does the problem statement say anything about which quadrant(s) $\beta$ and $\theta$ terminate?

I need to get back to you. I will look in the textbook.
 

FAQ: Which angle has a larger cosine value?

What is the difference between acute and obtuse angles?

An acute angle is less than 90 degrees, while an obtuse angle is greater than 90 degrees. In other words, an acute angle is smaller than a right angle, while an obtuse angle is larger than a right angle.

How do you measure angles?

Angles are measured in degrees using a protractor. Place the center of the protractor at the vertex of the angle, align one side of the angle with the baseline of the protractor, and then read the measurement where the other side of the angle intersects with the protractor.

What is a right angle?

A right angle is exactly 90 degrees. It is commonly represented by a small square in geometric diagrams.

How do you determine which angle is larger?

To determine which angle is larger, compare the measurements of the two angles. The angle with a greater measurement is larger. If the angles have the same measurement, they are equal.

Can an angle be larger than 180 degrees?

No, an angle cannot be larger than 180 degrees. This is because 180 degrees is a straight line, and any angle larger than that would result in overlapping lines. However, angles can be measured in multiples of 180 degrees, such as 270 degrees or 360 degrees.

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