Answer:
[tex]\sin \theta = 0.153[/tex], [tex]\cos \theta = 0.988[/tex], [tex]\tan \theta = 0.155[/tex], [tex]\cot \theta = 6.462[/tex], [tex]\sec \theta = 1.012[/tex], [tex]\csc \theta = 6.538[/tex]
Step-by-step explanation:
Let be the point [tex](x,y)[/tex], the six trigonometric functions of the angle are represented by following formulas:
[tex]\sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}}[/tex] (1)
[tex]\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}[/tex] (2)
[tex]\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{y}{x}[/tex] (3)
[tex]\cot \theta = \frac{1}{\tan \theta} = \frac{x}{y}[/tex] (4)
[tex]\sec \theta = \frac{1}{\cos \theta} = \frac{\sqrt{x^{2}+y^{2}}}{x}[/tex] (5)
[tex]\csc \theta = \frac{1}{\sin \theta} = \frac{\sqrt{x^{2}+y^{2}}}{y}[/tex] (6)
If we know that [tex]x = 84[/tex] and [tex]y = 13[/tex], then the values of the six trigonometric functions is:
[tex]\sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}}[/tex]
[tex]\sin \theta = 0.153[/tex]
[tex]\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}[/tex]
[tex]\cos \theta = 0.988[/tex]
[tex]\tan \theta = \frac{y}{x}[/tex]
[tex]\tan \theta = 0.155[/tex]
[tex]\cot \theta = \frac{x}{y}[/tex]
[tex]\cot \theta = 6.462[/tex]
[tex]\sec \theta = \frac{\sqrt{x^{2}+y^{2}}}{x}[/tex]
[tex]\sec \theta = 1.012[/tex]
[tex]\csc \theta = \frac{\sqrt{x^{2}+y^{2}}}{y}[/tex]
[tex]\csc \theta = 6.538[/tex]
