# Precalculus

Use one of the identities
cos(t + 2πk) = cos t or sin(t + 2πk) = sin t
(a)
sin(19π/4)

(b)
sin(−19π/4)

(c)
cos(11π)

(d)
cos(53π/4)

(e)
tan(−3π/4)

(f)
cos(π/4)

(g)
sec(π/6+ 2π)

(h)
csc(2π − 2π/3)

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1. here is how I do these ....
(perhaps you might find it easier in degrees, 19π/4 radians = 855°

sin(19π/4) = sin 855°
take away 2 rotations, (720° or 4π)
sin 19π/4 = sin 3π/4 = sin 135°
3π/4 or 135° is in quadrant II and π/4 or 45° from the x-axis
We also know that in II, the sine is positive
so sin 3π/4 = sin π/4 = sin 45° = 1/√2 or √2/2

.....

d) cos(53π/4) or cos 2385°
take away 12π or 2160°
cos 53π/4 = cos 5π/4 or cos 225°
This angle is in quad III making it negative and 45 from the x-axis

cos 53π/4 = - cos π/4 = -1/√2 or -√2/2

do the others the same way.

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2. cos11pi/6

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