An angle Ɵ in standard position for which terminal side passes through the point (-1, 2), how do you find the six trig functions for Ɵ?

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Answer 1 · 2016-10-22T19:32:50

Please see the explanation for the "How to".

Cartesian points can be specified using a radius, $r$ , and an angle, $theta$ , as follows:

$x = (r)cos(theta) and y = (r)sin(theta))$

$r = sqrt(x^2 + y^2)$

For the point $(-1, 2)$ :

$r = sqrt((-1)^2 + 2^2)$

$r = sqrt(5)$

Substitute this information into the equations for x and y:

$-1 = (sqrt(5))cos(theta) and 2 = (sqrt(5))sin(theta))$

$cos(theta) = -1/sqrt(5) and sin(theta) = 2/sqrt(5)$

Move the radicals to the numerators:

$cos(theta) = -sqrt(5)/5 and sin(theta) = 2sqrt(5)/5$

$sec(theta) = 1/cos(theta)$

$sec(theta) = -sqrt(5)$

$csc(theta) = 1/sin(theta)$

$csc(theta) = sqrt(5)/2$

$tan(theta) = y/x$

$tan(theta) = 2/-1$

$tan(theta) = -2$

$cot(theta) = 1/tan(theta)$

$cot(theta) = -1/2$