Question

Tan 3 x = 1. Find x​

Answer 1

By applying the mathematical definition of tangent:

tan

(

x

)

=

sin

(

x

)

cos

(

x

)

By using our demanded value:

sin

(

x

)

=

−

cos

(

x

)

By applying the trigonometric property:

cos

(

x

)

=

√

1

−

sin

(

x

)

2

sin

(

x

)

=

√

2

2

By using a calculator, the easy way, or interpolation, the hard way, we get:

arcsin

(

√

2

2

)

=

45

°

Remembering

x

=

3

⋅

x

we get the "basal" value: 135°. and apply:

x

=

135

±

n

⋅

180

where n is integer, you can get any other solution.

Answer 2

Let the number be x

3x = 1

x = 1/3