Question

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

Answer 1

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

Answer 2

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`