sin(70°)cos(10°) − cos(70°)sin(10°)
Use the formula
sin (A-B) = sin A cos B - cos A sin B
In this case, A = 70 and B = 10 degrees.
You should know what the sin of 60 is.
To calculate the value of sin(70°)cos(10°) − cos(70°)sin(10°), we need to use trigonometric identities. Specifically, we can use the angle subtraction formula, which states that sin(a - b) = sin(a)cos(b) - cos(a)sin(b).
Let's break down the expression step by step:
1. First, let's convert the given angles from degrees to radians. To convert from degrees to radians, we use the following formula: radians = degrees * (π/180).
- 70° in radians = 70 * (π/180) = (7π/18)
- 10° in radians = 10 * (π/180) = (π/18)
2. Now that we have the angles in radians, we can substitute them into the angle subtraction formula:
sin(70°)cos(10°) − cos(70°)sin(10°) = sin((7π/18) - (π/18))
3. Simplifying the expression inside the sine function:
(7π/18) - (π/18) = (6π/18) = (π/3)
4. Finally, we can calculate the sine of (π/3) using trigonometric values:
sin(π/3) = √3/2
So, sin(70°)cos(10°) − cos(70°)sin(10°) = √3/2.