Determine the value of cosine function if angle is 315 degrees .

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The value of cos 315 has to be determined.

cos 315 = cos (360 - 45)

=> cos (-45)

As cosine is an even function

=> cos 45

cos 45 = 1/sqrt 2

This gives cos 315 = 1/sqrt 2

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll express in radians the equivalent value of 315 degrees.

315 degrees = 7pi/4

We'll write 7pi/4 = pi + 3pi/4

We'll apply cosine function:

cos (7pi/4) = cos (pi + 3pi/4)

cos (pi + 3pi/4) = cos pi*cos (3pi/4) - sin pi*sin(3pi/4)

sin pi = 0 and cos pi = -1

cos (pi + 3pi/4) = - cos 3pi/4

cos 3pi/4 = cos (pi-pi/4) = cos pi*cos pi/4 + sin pi*sin pi/4

cos 3pi/4 = - cos pi/4 => - cos 3pi/4 = cos pi/4 = sqrt 2/2

cos (7pi/4) = sqrt 2/2

The value of cosine function if the angle is 315 degrees is sqrt2/2.

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