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.
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 the degree measurement to radians first.
To convert degrees to radians, we use the formula:
radians = degrees × π / 180
For an angle measuring 48°, the value in radians would be:
radians = 48 × π / 180
Simplifying this expression:
radians ≈ 0.83776π
Now, let's calculate the sine and cosine values for both the degree measurement and the radian measurement:
For an angle measuring 48°:
- Sine value: sin(48°)
- Cosine value: cos(48°)
For an angle measuring approximately 0.83776π:
- Sine value: sin(0.83776π)
- Cosine value: cos(0.83776π)
To determine if the two expressions are equivalent, let's calculate their values:
Calculating sin(48°):
sin(48°) ≈ 0.74314
Calculating cos(48°):
cos(48°) ≈ 0.66913
Calculating sin(0.83776π):
sin(0.83776π) ≈ 0.74314
Calculating cos(0.83776π):
cos(0.83776π) ≈ 0.66913
As we can see, the sine and cosine values for both the degree measurement and the radian measurement are approximately equal to each other. Thus, we have shown 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.
The value of the function is approximately 0.74314.