The basic trigonometric functions sine, cosine, and tangent give the ratio between two sides of a triangle with a given angle. The inverse trig functions find the angle if the ratio is known. Finding the inverse cosine often requires a calculator and more than five minutes if the side lengths are not given.
- Find the lengths of the triangle's sides
The cosine of an angle is the side adjacent to the angle divided by the right triangle's hypotenuse. Measure or calculate the lengths of the relevant sides (adjacent and hypotenuse).
- Examine the ratio
Divide the adjacent by the hypotenuse. This will give a fraction. Consider some of the properties of the cosine. If both the adjacent and hypotenuse are positive, the angle is between 0 and 90 degrees. Some common fractions for cosines of angles in degrees are: cos(0)=1 cos(30)=?3/2 so the inverse cosine of about 0.85 is close to 30 degrees; cos(45)=?2/2 so the inverse cosine of about 0.7 is close to 45 degrees; cos(60)=1/2 so the inverse cosine of 0.5 is 60 degrees. cos(90)=0 Determine whether you can determine the angle or approximate angle without a calculator.
- Use a calculator
If you cannot take inverse cosine based on the recognizable values, use a calculator. For many calculators, enter the quotient that you got by dividing the sides and select the alternate function of the cosine key (cos). For graphing calculators, enter the trig operation first and then input the fraction within parentheses. Check the calculator's answer to see if it makes sense according to the list above.