(i) sin 300° = sin(360° – 60°)
[For 360° – 60°. No change in T-ratio. 300° lies in 4th quadrant ‘sin’ is negative]
= -sin 60°
= - \(\frac{\sqrt{3}}{2}\)
(ii) cos(-210°) = cos 210° (∵ cos(-θ) = cos θ)
[∵ 180 + 30°. No change in T-ratio. 210° lies 3rd quadrant ‘cos’ is negative]
= cos(180° + 30°)
= -cos 30°
= - \(\frac{\sqrt{3}}{2}\)
(iii) sec 390° = sec(360° + 30°)
= sec 30°
= \(\frac{1}{cos 30°}\)
= \(\frac{1}{\frac{\sqrt{3}}{2}}\)
= \(\frac{2}{\sqrt{3}}\)
(iv) tan(-855°) = -tan 855° (∵ tan(-θ) = – tan θ)
[∵ Multiplies of 360° are dropped out. For 180° – 45°. No change in T-ratio. 180° – 45° lies in 2nd quadrant ‘tan’ is negative]
= -tan(2 x 360° + 135°)
= -tan 135°
= -tan(180° – 45°)
= -(-tan 45°)
= -(-1)
= 1
(v) cosec 1125° = cosec(3 x 360°+ 45°)
= cosec 45°
= \(\frac{1}{sin45°}\)
= \(\frac{1}{\frac{1}{\sqrt{2}}}\)
= √2
