Answer :
To find the angle [tex]\(a\)[/tex] when [tex]\(\cos a = \frac{14}{15}\)[/tex], we follow these steps:
1. Understand the relationship: The cosine function relates the angle [tex]\(a\)[/tex] in a right triangle to the ratio of the length of the adjacent side to the hypotenuse. Here, we're given [tex]\(\cos a = \frac{14}{15}\)[/tex].
2. Calculate the angle [tex]\(a\)[/tex]:
- To find the angle [tex]\(a\)[/tex], we use the inverse cosine function, also known as arccosine, which is denoted as [tex]\(\cos^{-1}\)[/tex]. The inverse cosine function allows us to find the angle whose cosine is a given number.
- So, [tex]\(a = \cos^{-1}\left(\frac{14}{15}\right)\)[/tex].
3. Express the angle in radians:
- The inverse cosine function will give us the angle [tex]\(a\)[/tex] in radians. In this case, [tex]\(a \approx 0.3672\)[/tex] radians.
4. Convert the angle to degrees:
- Since angles are often expressed in degrees, you can convert from radians to degrees using the conversion factor [tex]\(180^\circ/\pi\)[/tex].
- Thus, [tex]\(a \approx 21.04^\circ\)[/tex].
In summary, the angle [tex]\(a\)[/tex] for which [tex]\(\cos a = \frac{14}{15}\)[/tex] is approximately [tex]\(0.3672\)[/tex] radians or [tex]\(21.04^\circ\)[/tex].
1. Understand the relationship: The cosine function relates the angle [tex]\(a\)[/tex] in a right triangle to the ratio of the length of the adjacent side to the hypotenuse. Here, we're given [tex]\(\cos a = \frac{14}{15}\)[/tex].
2. Calculate the angle [tex]\(a\)[/tex]:
- To find the angle [tex]\(a\)[/tex], we use the inverse cosine function, also known as arccosine, which is denoted as [tex]\(\cos^{-1}\)[/tex]. The inverse cosine function allows us to find the angle whose cosine is a given number.
- So, [tex]\(a = \cos^{-1}\left(\frac{14}{15}\right)\)[/tex].
3. Express the angle in radians:
- The inverse cosine function will give us the angle [tex]\(a\)[/tex] in radians. In this case, [tex]\(a \approx 0.3672\)[/tex] radians.
4. Convert the angle to degrees:
- Since angles are often expressed in degrees, you can convert from radians to degrees using the conversion factor [tex]\(180^\circ/\pi\)[/tex].
- Thus, [tex]\(a \approx 21.04^\circ\)[/tex].
In summary, the angle [tex]\(a\)[/tex] for which [tex]\(\cos a = \frac{14}{15}\)[/tex] is approximately [tex]\(0.3672\)[/tex] radians or [tex]\(21.04^\circ\)[/tex].
