SOLUTION: If {{{ tan(x) = 4 / 5 }}} then, without a calculator, find {{{tan(pi / 2

SOLUTION: If {{{ tan(x) = 4 / 5 }}} then, without a calculator, find {{{tan(pi / 2 - x) }}}. Write your answer as a fraction.

Question 1203961: If then, without a calculator, find . Write your answer as a fraction.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

List of common trig identities
https://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

The identity we'll be using is

it is found at the bottom of page 2 under the subsection "Cofunction Formulas".

Cotangent is the reciprocal of tangent, meaning that if tan(x) = 4/5, then cot(x) = 5/4.
This then leads back to

---------------------------------------------------

Here is another approach.

Draw out a right triangle with these properties:
opposite = 4
adjacent = 5
theta = reference angle

We are then effectively given that tan(theta) = 4/5
The expression represents the other acute angle of this right triangle.
This is because the two acute angles add to pi/2 radians (aka 90 degrees). The acute angles are complementary.

With reference to angle , the positions of "opposite" and "adjacent" swap places.
This will mean that we have:
opposite = 5
adjacent = 4
pi/2 - theta = reference angle

Therefore, tan(pi/2 - theta) = opposite/adjacent = 5/4

Here is a diagram of what I refer to

RELATED QUESTIONS
If tan β = 4/5 then, without a calculator, find tan(𝛑/2 - β). Write your answer as a (answered by solver91311)

If tan β = 4/5 then, without a calculator, find tan( π/2 - β) and express the answer... (answered by ikleyn)

If {{{ cos(beta) = -3 / 5 }}} then, without a calculator, find {{{cos(pi / 2 - beta) }}}. (answered by mananth,ikleyn,MathLover1,MathTherapy)

If tan β=4/5, find tan(π/2-β) *Write your answer as a... (answered by ikleyn)

If cos β = - 3/5 then, without a calculator, find cos(𝛑/2 - β). Write your answer as (answered by Alan3354)

Find the exact value of x without using a calculator: tan x=-1,... (answered by stanbon)

Find tan ^-1 x for the given x. Express your answer as a rational multiple of pi, ranging (answered by Alan3354)

Solve the equation for 0≤x≤2pi. Write your answer as a multiple of pi, if... (answered by Alan3354)

Find sin (2x), cos(2x), and tan(2x) from the given information. Write your answer as a... (answered by Edwin McCravy)