What are the six trig function values of $420$ ?

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Answer 1 · 2018-03-11T09:10:45

Please read the explanation.

What are the six trigonometric function values of $color(red)(420^@$ ?

Given:

Angle $theta = 420^@$

We must find

$sin(420^@), cos(420^@), tan(420^@), csc(420^@), sec(420^@), and cot(420^@)$

Reference Angle is the angle measure from terminal side to x-axis.

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Hence, reference angle is $60^@$

It falls in the I quadrant where in all the six trigonometric functions are positive. as seen from the chart below.

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Special Right Triangle with $color(red)(30^@-60^@-90^@$

enter image source here

Now, we can write our six trigonometric functions:

$sin(420^@) = sqrt(3)/2$

$cos(420^@) = 1/2$

$tan(420^@) = sqrt(3)/1 or sqrt(3)$

$csc(420^@) = 2/sqrt(3) or (2sqrt(3))/3$

$sec(420^@) = 2/1 or 2" "$ and

$cot(420^@) = 1/sqrt(3) or sqrt(3)/3$

Hope it helps.

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