finding exact trig values for angles?

Question

who knows that exact values for these:
Sin Θ Cos Θ Tan Θ Csc Θ Sec Θ Cot Θ

for each of these angles:
0deg

30deg

45deg

60deg

90deg

Answer 1

sin 0 = cos 90 = 0
sin 30 = cos 60 = 1/2
sin 45 = cos 45 = (sqrt 2)/2
sin 60 = cos 30 = (sqrt 3)/2
sin 90 = cos 0 = 1

Now you can use those to find tan, csc, sec, and cot.

tan = sin / cos

csc = 1 / sin

sec = 1/ cos

cot = 1 / tan = cos / sin

Answer 2

sin 0 = 0
sin 30 = 1/2
sin 45 = [1/2]^1/2
sin 60 = (3^1/2)/2
sin 90 = 1

cos 0 =1
sin 60 = 1/2
sin 45 = [1/2]^1/2
sin 30 = (3^1/2)/2
sin 90 = 0

tan 0 = 0
tan30 = [1/3]^1/2
tan45 = 1
tan60 = 3^1/2
tan90 = infinite

cosec is the inverse (recprocal) of sin, sec is the inverse (recprocal) of cos and cot is the inverse (recprocal) of tan.

Answer 3

Exact Value

Sin30°= 1/2

Cos30°= √3 / 2

tan 30° = √3 / 3

csc30° = 2

sec30° = 2√3

cot30° = √3

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Exact value

45°

sin45° = √2 / 2

cos45° = √2 / 2

tan45° = 1

csc45° = √2

sec45° = √2

cot45° = 1

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Exact value

60°

sin60° = √3 / 2

cos60° = 1/2

tan60° = √3

csc60° = 2√3 / 3

sec60 °= 2

cot 60° = √3 / 3

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Exact value

90°

sin90° = 1

cos90° = 0

tan90° = Undefined

csc90° = 1

sec90° = undefined

cot90° = 0

- - - - - - - -s-

Answer 4

cos[(a million/2)x] = (-a million)^[[(x + ?)/(2?)]] * sqrt[(a million + cos(x))/2] The double brackets factor out the "least integer function". one hundred sixty 5*2 = 330 = 11?/6 radians. cos(11?/6) = sqrt(3)/2 [[(11?/6) + ?]/(2?)]] = a million. so... cos(11?/12) = (-a million)^a million * sqrt[(a million + sqrt(3)/2)/2] cos(11?/2) = -sqrt[(a million/2) + sqrt(3)/4] This fee is proper--it makes use of no decimal approximations

Answer 5

The best way is to draw an equilateral triangle to work out 30/60 and an isosoles one to work out 45, but here goes

Angle: Sine: Cosine: Tangent: Cosec: Sec: Cot
0............0...........1............0...........Inf.........1......Inf
30.......... .5 ...Sqr(3)/2 (Sqr(3)/3)..2.....2Sqr(3)/3 ... Sqr(3)
45......... sqr(2)/2 . sqr(2)/2 1: sqr(2)... sqr(2) .... 1
For angles > 45 reverse sines/ cosines secants/ cosecants and tangents/ cotangents