Trigonometric Ratios & Identities – Problems
1) Find the value of
i) sin (5π/4)
ii) tan (855°)
iii) tan [-23 π/3]
iv) sec (13 π/3)
Solutions:
i) Given that
sin (5π/4)
= sin [2π – (π/3)] (since sin (180 – x) = – sinx)
= – sin (π/3)
= (√3/2)
ii) Given that
tan (855°)
= tan [5 (180) – 45°]
= – tan 45° (since tan 45° = 1)
= -1
iii) Given that
tan [-23 π/3]
= – tan (23 π/3)
= – tan (6π + 5 π/3)
= – tan (5 π/3)
= – tan (2π – π/3)
= tan (π/3)
= √3
iv) Given that
sec (13 π/3)
= sec (4π + π/3)
= sec (π/3)
= 2
2) Convert the following into simplest form
i) tan (θ – 14π)
Solution: Given that tan (θ – 14π)
= – tan (14π – θ)
= tan θ
ii) cosec (5π + x)
Solution: Given that cosec (5π + x)
= cosec (4π + π + x)
= cosec (π + x)
= – cosec x