Question

If the terminal point determined by t is (-5,-4), then

\sin (t) =
;
\cos (t) =
;
\tan (t) =
.

Answer 1

The trigonometric ratios associated with (-5, -4) are
`\sin t \approx -0.625`,
`\cos t \approx -0.781` and
`\tan t = 0.8`.

Explanation:

Let
`\vec u = (x,y)`. From Trigonometry, we remember the following definitions for the trigonometric ratios, dimensionless:

`\sin t = \frac{y}{\sqrt{x^(2)+y^(2)}}` (1)

`\cos t = \frac{x}{\sqrt{x^(2)+y^(2)}}` (2)

`\tan t = (y)/(x)` (3)

If we know that
`x = -5` and
`y = -4`, then the trigonometric ratios are, respectively:

`\sin t = \frac{-4}{\sqrt{(-5)^(2)+(-4)^(2)}}`

`\sin t \approx -0.625`

`\cos t = \frac{-5}{\sqrt{(-5)^(2)+(-4)^(2)}}`

`\cos t \approx -0.781`

`\tan t = (-4)/(-5)`

`\tan t = 0.8`

The trigonometric ratios associated with (-5, -4) are
`\sin t \approx -0.625`,
`\cos t \approx -0.781` and
`\tan t = 0.8`.