Question

Sec0 = -
`(13)/(12)` and cot0 < 0, find exact values of tan0 and sin0.

Answer 1

tan 0 = -2.4

sin 0 = 0.3846

Explanation:

sec 0 = -13/12, and cot 0 < 0

the angle 0 is in quadrant II

sec 0 = -13/12 = cos 0 = -12/13 = x/r

=> y = √13²-12²=√169-144=√25=5

so,

tan 0 = y/x = -12/5 = -2.4

sin 0 = y/r = 5/13 = 0.3846

Answer 2

Solution given;

Sec θ=-
`(13)/(12)`

cotθ< 0,

It lies in second quadrant.

where sin and cosec is positive.

Now

`(1)/(cosθ)=-(13)/(12)`

cosθ=
`(12)/(13)`

`(b)/(h)`=
`(12)/(13)`

b=12

h=13

By using Pythagoras law

p=
`√(13²-12²)=5`

Now

exact values of tan θ=
`(p)/(b)`=
`(5)/(12)`

since it lies in II quadrant

tan θ=-
`(5)/(12)`

and

sinθ=
`(p)/(h)`=
`(5)/(13)`

since it lies in II quadrant

sin θ=
`(5)/(13)`