**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