Hi,how do I find both solutions of the equation cos0 = 0.35 between degrees 0 and 360?
Many thanks
the cosine is positive in the I and IV quadrant
using the inverse cosine function on your calculator
Ø = 69.513°
so Ø is either 69.513° or (360-69.513)° or 290.487°
i hope this is not ou question? as this is the exam cheat
i hope this is not ou question? as this is the exam cheat ...... YOU
To find the solutions of the equation cos0 = 0.35 between 0 and 360 degrees, you need to use the inverse cosine function (cos^-1) or the arc cosine function (acos).
Step 1: Convert 0.35 to its corresponding angle value using a calculator.
- Enter 0.35 in the calculator.
- Use the inverse cosine or arc cosine function (cos^-1 or acos) to find the corresponding angle in radians.
- You will get the angle value in radians, which we'll call A.
Step 2: Convert the angle value from radians to degrees.
- Multiply the angle value (A) by 180 and divide by π (pi) to convert it from radians to degrees.
- You will get the angle value in degrees, which we'll call B.
Step 3: Find the first solution by adding angle B to 0 degrees.
- Add angle B to 0 degrees. This will give you the first solution.
Step 4: Find the second solution by subtracting angle B from 360 degrees.
- Subtract angle B from 360 degrees. This will give you the second solution.
Now, let's go through an example:
Step 1: Using a calculator, cos^-1(0.35) = 1.166 rad (approximately).
Step 2: Convert from radians to degrees: (1.166 rad) x (180/π) = 66.789 degrees (approximately).
Step 3: First solution: 0 degrees + 66.789 degrees = 66.789 degrees.
Step 4: Second solution: 360 degrees - 66.789 degrees = 293.211 degrees (approximately).
Therefore, the solutions for the equation cos0 = 0.35 between 0 and 360 degrees are approximately 66.789 degrees and 293.211 degrees.