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Trigonometry: Simple Trigonometric values
Without using your calculator (and writing √x as sqrt(x) and ∞ as Infinity),
give the exact value of
cos( –405°) =

tickcross



Worked Solution

Equivalent 0-360° angle:
The angle is negative so we can add on 360° to make it positive:
2×360 – 405 = 315
=> –405° is the same angle as 315°
Basic angle:
From the symmetry of the cosine graph, the angle between 0 and 90° with the same cosine as 315° is 45°
Cosine value:
From the 45-45-90 diagram, we have
cos(45°) =
1
---
2
√2

ASTC quadrantsQuadrant and Sign:
The angle 315° is in the fourth quadrant (270°-360°).
From the ASTC diagram, cosines of angles in this quadrant have the sign: +

cos( –405°) = cos(315°) = cos(45°) =
1
---
2
√2
 = 0.707 to 3 dps

sin cos graphs
45-45-90 triangle has sides 1,1,sqrt(2)

© MEI Produced by Dr Ron Knott, 13 June 2008
tom . button [AT] mei . org . uk 		Test reference: TrigSimpleValues.html?ref=4146