How do you find the six trigonometric functions of 315 degrees?

2 Answers
Nghi N.
Jul 18, 2015

Find 6 trig functions of (315)

Explanation:

On the trig unit circle,
sin (315) = sin (-45 + 360) = sin (-45) = - sin (45)
Trig table gives -> sin 315 = -sin 45 = -(sqrt2)/2
cos 315 = cos (- 45) = cos 45 = (sqrt2)/2
tan 315 = sin/(cos) = - 1
cot 315 = 1/tan = -1
sec = 1/cos = sqrt2
csc = 1/sin = - sqrt2

Dean R.
May 11, 2018

This is one of the usual suspects, -45^circ, in the fourth quadrant, positive cosine, negative sine:

cos(315^circ) =1/sqrt{2}

sin(315^circ) = -1/sqrt{2}

tan 315^circ = -1

sec 315^circ = sqrt{2}

csc 315^circ = -sqrt{2}

cot 315^circ = -1

Explanation:

Step 1: First we fight the depression that comes when we see they've asked yet again a question about the two tired triangles of trig, 30/60/90 or 45/45/90.

Step 2: We apply various trig identities related to coterminal and negated angles and do the problem.

cos(315^circ) = cos(315^circ - 360^circ ) = cos(-45^circ) = cos 45^circ = 1/sqrt{2}

Typing that is like practicing scales on the piano. Question writers, please give us another triangle.

sin(315^circ) = sin(315^circ - 360^circ ) = sin(-45^circ) = -sin 45^circ = -1/sqrt{2}

tan 315^circ = {sin 315^circ}/{cos 135^circ} ={-1/sqrt{2} }/{1/sqrt{2} } = -1

sec 315^circ = 1/{cos 315^circ }= sqrt{2}

csc 315^circ = 1/ {sin 315^circ }= -sqrt{2}

cot 315^circ = 1/ {tan 315^circ }= -1

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