The cosine of the angle is \(\cos(\theta) = \frac {5}{\sqrt{41}}\), the cosecant is \(\csc(\theta) = -\frac{\sqrt{41}}{4}\) and the tangent is \(\tan(\theta) = -\frac 54\)
How to evaluate the trigonometry expressions?
The terminal side is given as:
(x, y) = (5, -4)
Start by calculating the radius (r) using
\(r = \sqrt{x^2 + y^2\)
This gives
\(r = \sqrt{5^2 + (-4)^2\)
Evaluate
\(r = \sqrt{41\)
The cosine of the angle is calculated using:
\(\cos(\theta) = \frac xr\)
This gives
\(\cos(\theta) = \frac {5}{\sqrt{41}}\)
The cosecant is calculated using:
\(\csc(\theta) = \frac{r}{y}\)
This gives
\(\csc(\theta) = -\frac{\sqrt{41}}{4}\)
The tangent is calculated using:
\(\tan(\theta) = \frac yx\)
This gives
\(\tan(\theta) = -\frac 54\)
Read more about terminal side at:https://brainly.com/question/1982296
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