How do you write the 6 trig values in exact form for the acute angle formed by the line passing through the point: P(3, 4)?

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Answer 1 · 2016-10-31T09:53:13

The sides of the triangle are $3, 4, 5$
Now you can write the ratios.

I assume the line you are referring to also goes through the origin?

The triangle thus formed is a right-angled triangle and you can use Pythagoras' Theorem to find the length of the hypotenuse:

$3^2+4^2 = 25 = 5^2 rarr h = 5$

So for the acute angle $(hatA)$ formed between the $x-$ axis and the hypotenuse, the sides are:

$opp = 4, adj = 3 and hyp = 5$

Now you can write down the 6 ratios:

$sin hatA = 4/5," "cos hatA = 3/5" " tan hatA = 4/3$

$cosec hatA = 5/4," "sec hatA = 5/3" " cot hatA = 3/4$