# Inverse trigonometry

Related Topics:
More Lessons for Trigonometry, Math Worksheets

If we know the size of an angle, we can find the sin, cos and tan of the angle by using a scientific calculator. We can also use a calculator to find the inverse or reverse of this. If we know the sin, cos or tan of an angle, we can find the size of the angle.

If tan θ = x then tan -1 x = θ

If sin θ = x then sin -1 x = θ

If cos θ = x then cos -1 x = θ

Example:

Find the values of θ for the following (Give your answers in degrees and minutes):

a) tan θ = 2.53

b) sin θ = 0.456

c) cos θ = 0.6647

Solution:

a) Press

tan -1 2.53 = 68˚ 25 ’ 59.69 ” ( The ” symbol denotes seconds. There are 60 seconds in 1 minute.)

= 68˚ 26 ’ (to the nearest minute)

b) Press

sin -1 0.456 = 27˚ 7 ’ 45.46 ”

= 27˚ 8 ’ (to the nearest minute)

b) Press

cos -1 0.6647 = 48˚ 20 ’ 26.47 ”

= 48˚ 20 ’ (to the nearest minute)

Example:

Calculate the angle x in the figure below. Give your answer correct to 4 decimal places.

Solution:

sin x =

x = sin -1(2.3 ÷ 8.15)

= 16.3921˚

The following video shows how to use a calculator to obtain the size of an angle given the trigonometry ratio.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.