How do you find the exact value of the six trigonometric functions of the angle whose terminal side passes through $(-0.5, 4.5)$ ?

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Answer 1 · 2018-02-27T09:48:35

As below.

$x = -0.5, y = 4.5$

$r = sqrt(x^2 + y^2) = sqrt((-1/2)^2 + (9/2)^2 )= sqrt(82/4)= sqrt(41/2)$

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$sin alpha = y / r = (9/2) / sqrt(41/2) = 9 / sqrt82$

$cos alpha = x / r = -(1/2) / sqrt(41/2) = -(1/sqrt82)$

$tan alpha = y / x = -(9/2) / (1/2) = -9$

$csc alpha = 1 / sin alpha = sqrt82 / 9$

$sec alpha = 1/cos alpha = - sqrt82$

$cot alpha = -(1/9)$

How do you find the exact value of the six trigonometric functions of the angle whose terminal side passes through (-0.5, 4.5)(-0.5, 4.5)?