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