Find the values of the following trigonometric ratios : `cos225^@`, `sin 690^@`, `tan(-390^@)`, `sec 855^@`

Options

A. `cos225^@`
B. `sin 690^@`
C. `tan(-390^@)`
D. `sec 855^@`

Explanation

(i) For angle `225^@`, terminal side of angle lies in third quadrant where cosine function is negative.
`:. cos225^@=cos(90^@xx2+45^@)=-cos45^@=-1/sqrt2`
(ii) For angle `690^@`, terminal side of angle lies in fourth quadrant where side function is negative.
`:. sin690^@=sin(90^@xx7+60^@)=-cos60^@=-1/2`
(iii) For angle `390^@`, terminal side of angle lies in first quadrant where tan function is positive.
`:. tan-390^@)=-tan390^@`
`=-tan(90^(@)xx4+30^@)`
`=-tan30^@=-1/sqrt3`
(iv) For angle `855^@`, terminal side of angle lies in second quadrant where secant is negative.
`:. sec885^@=sec(90^@xx9+45^@)=-sec45^@=-sqrt2`