How do i get the exact value of sec 225°?

2 Answers
Apr 26, 2018

sec225° = -sqrt2

Explanation:

Apply the identity sectheta=1/(costheta)

sec225° = 1/(cos225°)

1/(cos225°) = 1/(cos(180°+45°)

Use the angle sum identity cos(a+b)=(cosa ⋅ cosb)-sina ⋅ sinb)
where a=180° and b=45°

1/(cos(180°+45°)=1/((cos180° ⋅ cos45°) - (sin180° ⋅ sin45°))

cos180°=-1

cos45°=(√2) / 2

sin180°=0

sin45°=(√2) / 2

1/((cos180° ⋅ cos45°) - (sin180° ⋅ sin45°))=1/((-(√2) / 2)-0

1/((-(√2) / 2)=-2/sqrt2

Rearrange the equation so there is no square root in the denominator

-2/sqrt2sqrt2/sqrt2 = -(2sqrt2)/2 = -sqrt2

Apr 26, 2018

- sqrt2

Explanation:

Use trig identity:
cos (a + b) = cos a.cos b - sin a. sin b
In this case -->
cos 225 = cos (180 + 45) = cos 180.cos 45 - sin 180.sin 45.
Since: sin 180 = 0; cos 180 = -1, and cos 45 = sqrt2/2, therefor:
cos 225 = (-1)sqrt2/2 = - sqrt2/2
sec 225 = 1/(cos 225) = - 2/(sqrt2) = - sqrt2
Check by calculator.
cos 225 = - 0.707 --> sec 225 = 1/0.707 = 1.414
sec 225 = -sqrt2 = - 1.414 . Proved.