Unit Circle

(Cos,Sin)

(1,0)

tan

Sin/Cos

Whats ASTC (ALL STUDENTS TAKE CALCULUS)

Sin, All, Tangent, Cosine

All (Sin, Tangent, Cosine)

Q1 All Sin/Tangent/Cosine is positive

STUDENTS (Sin)

Q2 Only Sin is positive all others are negative

TAKE (Tangent)

Q3 Only Tangent is positive all others are negative

Calculus (Cosine)

Q4 Only Cosine is positive all others are negative

Angles

They go from 0 to 330. Quadrants add 90. The numbers in the quandrants start by adding 30, then add 15. Then add 30 again.

Q1: 0, 30, 45, 60, 90

Q2: 90, 120, 135, 150, 180

Q3: 180, 210, 225, 240, 270

Q4: 270, 300, 315, 330, 0

π=180 degrees

so π/2 is 180/2 which is 90

30 is the same as π/6

150 is the same as 5π/6

210 is the same as 7π/6

11π/6 is the same as 330

45 is π/4

135 is 3π/4

225 is 5π/4

315 is 7π/4

60 is π/3

120 is 2π/3

240 is 4π/3

300 is 5π/3

90 is π/2

180 is π

270 is 3π/2

0 and 360 are co term angles. the same as 2π

Xy coordinates for angle 0 is (1,0) In Q1

30 is (√3/2, 1/2)

45 is (√2/2, √2/2)

60 is (1/2, √3/2)

90 is (0,1) But for Q2 the x coordinates (Cosine) are negative

120 is (-1/2,√3/2)

135 is (-√2/2, √2/2)

150 is (-√3/2, 1/2)

180 is (-1,0)

210 is (-√3/2, -1/2) All negative in the third Quadrant but it’s the same as q1

225 is (-√2/2, -√2/2)

240 is (-1/2, -√3/2)

270 is (0,-1) In Q4, it’s the reveser of Q1 but the y (sin) is negative

300 is (1/2, -√3/2)

315 is (√2/2,-√2/2)

330 is (√3/2,-1/2)

Triangles

30 60 90

SOH CAH TOA

Sin opposite divided by hypotenuse, cosine adjacent over hypotenuse tangent oppositive over adjacent

triangle 2

45 45 90

Unit circle

circle