How to get 5degree without using calculator using identities?
To find the value of sin(5°) without using a calculator, you can use the sum of angles formula or the half-angle formula.
Method 1: Sum of Angles Formula
The sum of angles formula states that sin(A + B) = sin(A)cos(B) + cos(A)sin(B).
In this case, we can represent 5° as the sum of two angles, 3° and 2°: 5° = 3° + 2°.
Now, substitute the values into the formula: sin(3° + 2°) = sin(3°)cos(2°) + cos(3°)sin(2°).
Using the known values of sin(3°) and cos(3°) from trigonometric tables (or a previous calculation), you can find the values of sin(3°) and cos(3°).
Finally, substitute the values back into the equation to find sin(5°).
Method 2: Half-Angle Formula
The half-angle formula for sine states that sin(x/2) = ±√[(1 - cos(x))/2], where x is the angle in radians.
To convert 5° to radians, you'll need to multiply it by π/180: 5° × π/180 = (5π)/180 radians.
Now, substitute (5π)/180 into the formula: sin((5π)/180/2) = ±√[(1 - cos((5π)/180))/2].
Using the known values of cos((5π)/180) from trigonometric tables (or a previous calculation), you can find the value of cos((5π)/180).
Finally, substitute the value back into the equation to find sin(5°).
Note: It is important to recognize that these methods result in approximate values due to the reliance on trigonometric tables (or previous calculations) for known angle values.