show that the sine of cosine value of an angle measuring 48° is equivalent to the sine or cosine value of that same angle measured in radians and state the value of the function. answer like a 11th grader.
To show that the sine of the cosine value of an angle measuring 48° is equivalent to the sine or cosine value of that same angle measured in radians, we need to convert 48° to radians.
In order to convert degrees to radians, we know that π radians is equivalent to 180°. Therefore, we can create a proportion to find the radian measure of 48°:
π radians x radians
--------- = ----------
180° 48°
Cross multiplying the proportion, we get:
180° * x radians = π radians * 48°
Simplifying the equation, we have:
180x = 48π
Dividing both sides by 180, we find:
x ≈ 0.840
So, the angle measuring 48° is equivalent to approximately 0.840 radians.
Now, let's find the sine and cosine values for both 48° and 0.840 radians.
Using a calculator, we find that the sine of 48° is approximately 0.743 and the cosine of 48° is approximately 0.669.
Using the same calculator, we find that the sine of 0.840 radians is approximately 0.744 and the cosine of 0.840 radians is approximately 0.669.
Hence, the sine and cosine values of the angle measured in degrees and radians are very close and almost equivalent. In this case, the sine or cosine value of an angle measuring 48° is approximately 0.743 or 0.669, which is almost equal to the sine or cosine value of the same angle measured in radians, which is approximately 0.744 or 0.669.