SOLUTION: If tan β = 4/5 then, without a calculator, find tan(𝛑/2 - β). Write your answer as a fraction please.
Thank You
Algebra.Com
Question 1145658: If tan β = 4/5 then, without a calculator, find tan(𝛑/2 - β). Write your answer as a fraction please.
Thank You
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The formula for the tangent of the difference of two angles, namely:
\ =\ \frac{\tan\alpha\,-\,\tan\beta}{1\ +\ \tan\alpha\tan\beta})
fails us in this instance because 
is undefined. Pity.
However, recall that 
, hence
So:
)
Similarly,
Now we can use the difference formulas for sine and cosine to calculate
)
And
)
Since 
, the signs of sine and cosine must be the same.
And
Then
\ =\ \frac{\pm\frac{5}{\sqrt{41}}}{\pm\frac{4}{\sqrt{41}}}\ =\ \frac{5}{4})
John
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
If {{{ tan(x) = 4 / 5 }}} then, without a calculator, find {{{tan(pi / 2 - x) }}}. Write... (answered by math_tutor2020)
If tan β = 4/5 then, without a calculator, find tan( π/2 - β) and express the answer... (answered by ikleyn)
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)
If {{{ cos(beta) = -3 / 5 }}} then, without a calculator, find {{{cos(pi / 2 - beta) }}}. (answered by mananth,ikleyn,MathLover1,MathTherapy)
Evaluate without using a calculator.
sin θ, if cos θ = 2/5 and tan θ < 0. (answered by lwsshak3)
If cos β = -3/5 then, without a calculator, find cos( π/2 - β) and express your answer (answered by solver91311)
Without using a calculator, find the exact value as fraction (not a decimal... (answered by stanbon)
Given tan θ = -5/12 and cos θ > 0, find csc θ. Write your answer as a... (answered by josgarithmetic,Theo)