Without the use of the calculator
.23 degrees + sin 37 degrees
Check your typing of the question, I don't see any way to do this.
Perhaps you meant
sin23° + sin37°
we have : sinA + sinB = 2sin((A+B)/2)cos((A-B)/2)
sin23° + sin37°
= 2sin((37+23)/2) cos((37-23)/2)
= 2 sin 30° cos 7°
= 2(1/2)cos7°
= cos7°
I don't see 7° as one of the usual angles associated with "exact" values, but my result is correct up to that point
To solve this equation without a calculator, you can use the trigonometric identity that relates the sine function to degrees. The identity states that sin(θ) = cos(90° - θ).
First, convert 0.23 degrees to radians by multiplying it by π/180:
0.23° * π/180 ≈ 0.004014257538 radians
Then, find the cosine of (90° - 37°):
cos(90° - 37°)
Since 90 - 37 = 53, we have:
cos(53°)
Now, we can use the cosine value of 53° to find the sine of 37° using the trigonometric identity sin(θ) = cos(90° - θ):
sin(37°) = cos(53°) ≈ 0.601815023
Finally, add 0.23 degrees to the sine value of 37°:
0.23° + sin(37°) ≈ 0.23° + 0.601815023 ≈ 0.831815023
Therefore, approximately, 0.23 degrees + sin(37 degrees) is equal to 0.831815023.