Find the values of the six trigonometric functions of an angle in standard position if the point with coordinates (84, 13) lies on its terminal side.

Question

asked Sep 7, 2022 198k views

1 Answer

Nathanael Demacon · Answer 1 · 2022-09-10T23:03:15+0000

Answer:

$\sin \theta = 0.153$ ,
$\cos \theta = 0.988$ ,
$\tan \theta = 0.155$ ,
$\cot \theta = 6.462$ ,
$\sec \theta = 1.012$ ,
$\csc \theta = 6.538$

Explanation:

Let be the point
(x,y) , the six trigonometric functions of the angle are represented by following formulas:

$\sin \theta = \frac{y}{\sqrt{x^(2)+y^(2)}}$ (1)

$\cos \theta = \frac{x}{\sqrt{x^(2)+y^(2)}}$ (2)

$\tan \theta = (\sin \theta)/(\cos \theta) = (y)/(x)$ (3)

$\cot \theta = (1)/(\tan \theta) = (x)/(y)$ (4)

$\sec \theta = (1)/(\cos \theta) = \frac{\sqrt{x^(2)+y^(2)}}{x}$ (5)

$\csc \theta = (1)/(\sin \theta) = \frac{\sqrt{x^(2)+y^(2)}}{y}$ (6)

If we know that
x = 84 and
y = 13 , then the values of the six trigonometric functions is:

$\sin \theta = \frac{y}{\sqrt{x^(2)+y^(2)}}$

$\sin \theta = 0.153$

$\cos \theta = \frac{x}{\sqrt{x^(2)+y^(2)}}$

$\cos \theta = 0.988$

$\tan \theta = (y)/(x)$

$\tan \theta = 0.155$

$\cot \theta = (x)/(y)$

$\cot \theta = 6.462$

$\sec \theta = \frac{\sqrt{x^(2)+y^(2)}}{x}$

$\sec \theta = 1.012$

$\csc \theta = \frac{\sqrt{x^(2)+y^(2)}}{y}$

$\csc \theta = 6.538$