INVERSE TRIGONOMETRY

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.

Custom Search

Useful Links:
Trigonometry