Let theta be 315 degrees. How do you find the exact values of tan theta, sin theta, and sec theta

tan 315 =
sin 315 =
sec 315 =


I need help with this question! I can't remember how to do it... Can anyone help me out? Please and thank you!

315° = 360° – 45° Let α=360 and β = 45

sin α – β = sin α cos β – sin β cos α =

sin 360 cos 45 – sin 45 cos 360 =

0•cos 45 – √2/2 •1 = –√2/2

Similarly plug into

tan α– β = (tan α – tan β)/(1 + tan α tan β)

and

sec α–β = 1/cos α–β = 1/(cos α cos β + sin α sin β )

OR The Eeeeasy way-- just draw a 45 degree angle in the 4th quadrant and read the answers from the triangle: The legs are +1 and –1 and the hypotenuse is √2.

tan 315 = –1
sin 315 = –1/√2 = –√2/2
sec 315 = √2/1 = √2

Reference angle = 45 degrees

45 degree angle is in Q1, where y > 0
315 degree angle is in Q4, where y < 0
sin(315) = −sin(45) = −√2/2

In Q1, x > 0
In Q4, x > 0
cos(315) = cos(45) = √2/2

tan(315) = sin(315)/cos(315) = (−√2/2)/(√2/2) = −1

cot(315) = 1/tan(315) = −1

sec(315) = 1/cos(315) = 2/√2 = √2

csc(315) = 1/sin(315) = −2/√2 = −√2

Mαthmφm