Getting ready for Pre-Calculus class.

From Geometry: Special triangles

π/2 𝜋/3 60° 𝜋 3 𝜋/4 45° 𝜋/6 𝜋 4 30° 𝜋 6 2𝜋/3 3𝜋/4 𝜋 5𝜋/6 𝜋 2𝜋 7𝜋/6 Angle/degrees Angle/radians  sin cos  tan cot 0    30  45  60  90  120  135  150  180 210  225  240   270  300  315 330  360  𝜋/3 60° 𝜋 3   𝜋 2 𝜋/4 90  45° 𝜋 4 𝜋/6 π/2 30° 𝜋 6 2𝜋/3 3𝜋/4 𝜋  180 5𝜋/6 0  𝜋  2𝜋 360 7𝜋/6 5𝜋/4 4𝜋/3 3𝜋/2  3𝜋 2    270 5𝜋/3 7𝜋/4 11𝜋/6 2𝜋

𝑦= sin 𝑥 =𝑜𝑝𝑝/ℎ𝑦𝑝 𝑦= cos 𝑥 =𝑎𝑑𝑗/ℎ𝑦𝑝 𝑦= tan 𝑥 = sin 𝑥 cos 𝑥 =𝑜𝑝𝑝/𝑎𝑑𝑗 𝑦= cot 𝑥 = cos 𝑥 sin 𝑥 =𝑎𝑑𝑗/𝑜𝑝𝑝

One more time 1 2 2 2 3 2 1 3 2 2 2 1 2 1 1 3 3 1 1 3 1 3

θ 𝜋 2 𝜋 3𝜋 2 2𝜋 𝑦=sin⁡(𝑥) 𝜋 2 𝑦=𝑠𝑖𝑛𝑥 𝜋 2𝜋 3𝜋 2 sin 3𝜋 2 =−1 sin 𝜋 2 =1 2𝜋 3𝜋 2 θ 𝜋 2 𝜋 3𝜋 2 2𝜋 𝑦=sin⁡(𝑥) sin 3𝜋 2 =−1 sin 𝜋 2 =1 sin 0 =0 sin 𝜋 =0 sin 2𝜋 =0

θ 𝜋 2 𝜋 3𝜋 2 2𝜋 𝑦=cos⁡(𝑥) 𝜋 2 𝑦=cos⁡(𝑥) 𝜋 2𝜋 3𝜋 2 cos 𝜋 2 =0 2𝜋 3𝜋 2 θ 𝜋 2 𝜋 3𝜋 2 2𝜋 𝑦=cos⁡(𝑥) cos 𝜋 2 =0 cos 3𝜋 2 =0 cos 𝜋 =−1 cos 2𝜋 =1 cos 0 =1

𝑦= sin⁡(𝜋/2) cos⁡(𝜋/2) = 1 0 =undefined 𝑦=tan⁡(𝑥) 𝜋 2 𝜋 4 𝜋 2𝜋 3𝜋 2 𝑦= tan 𝑥 = sin⁡(𝑥) cos⁡(𝑥) 𝑦= tan 𝑥 = sin⁡(0) cos⁡(0) = 0 1 =0 𝑦= sin⁡(3𝜋/2) cos⁡(3𝜋/2) = −1 0 =𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑦= sin⁡(𝜋/4) cos⁡(𝜋/4) = 2 /2 2 /2 =1 𝑦= sin⁡(𝜋/2) cos⁡(𝜋/2) = 1 0 =undefined 𝑦= tan 𝑥 = sin⁡(𝜋) cos⁡(𝜋) = 0 1 =0

𝑦=cot⁡(𝑥) 𝜋 2 3𝜋 4 𝜋 4 𝜋 2𝜋 3𝜋 2 𝑦= cot 𝑥 = cos⁡(𝑥) sin⁡(𝑥) 𝑦= cot 𝑥 = cos⁡(𝜋/2) sin⁡(𝜋/2) = 0 1 =0 𝑦= cot 𝑥 = cos⁡(𝜋/4) sin⁡(𝜋/4) = 2 /2 2 /2 =1 𝑦= cot 𝑥 = cos⁡(0) sin⁡(0) =𝑢𝑛𝑑𝑒𝑓 𝑦= cot 𝑥 = cos⁡(3𝜋/4) sin⁡(3𝜋/4) = 2 /2 2 /2 =−1 𝑦= cot 𝑥 = cos 𝜋 sin⁡(𝜋) =𝑢𝑛𝑑𝑒𝑓