Question

Evaluate sec960°.
1. -2
2. - 2 sqrt3/3
3. 2sqrt 3/3
4. 2

Answer 1

Option 1. ( -2)

Explanation:

sec (960°)

= sec [ 360 × 2 + 180 + 60° ]

This signifies when we draw 960° it revolves 360° twice 180° once then 60° in third quadrant in positive direction.

That means sec 960 = -(sec60)

=
`-((1)/(cos60))`

=
`(-1)/((1)/(2) )`

= (-2)

Option 1. ( -2) is the answer.

Answer 2

-2

Explanation:

We want to evaluate;

`\sec960\degree`

We use the reciprocals of trigonometric ratios to obtain;

`\sec960\degree=(1)/(\cos960\degree)`

The 960 degree angle makes an angle of 60 degree with the positive direction of the x-axis and it is in the 3rd quadrant.

This implies that;

`\sec960\degree=(1)/(-\cos60\degree)`

We use special trigonometric ratios to obtain;

`\sec960\degree=(1)/(-(1)/(2))`

`\sec960\degree=-2`