Question

The value of cos(– 870°) is ______.

Options

• `-1/4`

• `-sqrt(3)/2`

• `1/sqrt(2)`

• 1

Answer 1

The value of cos(– 870°) is `underlinebb(-sqrt(3)/2)`.

Explanation:

cos(– 870°) = cos 870°  ...[∵ cos(– θ) = cos θ]

= cos(720° + 150°)

 = cos(2 × 360° + 150°)  ...[∵ cos(n × 360° + θ) = cos θ, n ∈ Z]

= cos 150°  

= cos(180° – 30°)  ...[∵ cos(180° – θ) = – cos θ]

= – cos 30°  

= `- sqrt(3)/2`