(Cos40-sin30)/(sin60-cos50)
recall your sum formulas.
cos40-sin30 = cos40-cos60 = 2 sin50 sin10
sin60-cos50 = cos30-cos50 = 2 sin40 sin10
so, you end up with sin50/sin40
To simplify the expression (cos40 - sin30)/(sin60 - cos50), we can start by simplifying the individual trigonometric ratios.
1. Simplifying cos(40):
Since cos(40) is a specific angle, we need to use a calculator or reference table to find its value. In this case, cos(40) is approximately 0.766.
2. Simplifying sin(30):
Similar to cos(40), sin(30) is a specific angle. Using a calculator or reference table, we find that sin(30) is 0.5.
3. Simplifying sin(60):
Again, using a calculator or reference table, sin(60) is also 0.866.
4. Simplifying cos(50):
Lastly, cos(50) can be determined using a calculator or reference table. It is approximately 0.643.
After substituting the values we have found into the expression, we get:
(0.766 - 0.5)/(0.866 - 0.643)
Now, we can simplify this further:
(0.266)/(0.223)
Simplifying this division gives us:
1.19
Therefore, (cos40 - sin30)/(sin60 - cos50) simplifies to approximately 1.19.
To simplify the expression (cos40-sin30)/(sin60-cos50), we can start by calculating the values of cos40, sin30, sin60, and cos50.
To do this, we need to use trigonometric values.
1. cos40: Use a calculator or trigonometric table to find the cosine value of 40 degrees. Let's assume it to be a decimal value of x.
2. sin30: Use a calculator or trigonometric table to find the sine value of 30 degrees. Let's assume it to be a decimal value of y.
3. sin60: Use a calculator or trigonometric table to find the sine value of 60 degrees. Let's assume it to be a decimal value of z.
4. cos50: Use a calculator or trigonometric table to find the cosine value of 50 degrees. Let's assume it to be a decimal value of w.
Now, we substitute these values back into the original expression:
(cos40-sin30)/(sin60-cos50)
= (x - y)/(z - w)
This is the simplified expression using the decimal values of cos40, sin30, sin60, and cos50 that we calculated.