Could someone help me with this question please?
Which angle between 0° and 360° has the same cosine as the angle 55°?
Thanks in advance
the cosine is positive in the first and fourth quadrant,
so cos 55° = cos(360°-55°)
= cos 305°
test it with your calculator.
Certainly! To find the angle between 0° and 360° that has the same cosine as the angle 55°, we can use the fact that the cosine function has a periodicity of 360°. This means that if two angles have the same cosine value, they will differ by a multiple of 360°.
To solve the problem, we need to find the angle within the range of 0° to 360° that has the same cosine value as 55°.
First, we need to find the cosine of 55°. You can use a scientific calculator or an online calculator to find the cosine of 55°, which is approximately 0.57358.
Now, we need to find the angle within the desired range that has this same cosine value. To do this, we can use the inverse cosine function (also known as arccosine) to find the angle.
Using the inverse cosine function or the arccosine function, you can find the angle whose cosine is equal to 0.57358.
Using a calculator, you can input the cosine value (0.57358) and take the inverse cosine (arccosine) to find the angle.
arccos(0.57358) ≈ 55°
Since the cosine function is periodic with a period of 360°, we can deduce that the angle 55° is already within the range of 0° to 360° and has the same cosine value. Therefore, the angle between 0° and 360° that has the same cosine as 55° is 55° itself.
I hope this clarifies the solution and helps you understand how to approach similar problems in the future.