Precalc Midterm #1

Graphs of sin / cos

y = a*sin(b(x-c) + d or y = a*cos(b(x-c) + d

A = amp ((max + min) / 2)

B → period = 2pi / B

• period = one full cycle of the graph

C = horizontal shift

D = midline

Sin starts at 0 / midline

Cos starts at 1 / maximum

Graphs of tan

y = a*tan(b(x-c)

No amp / a = vertical stretch

Period = pi / B

• ticks = period / 2

C = horizontal shift

D = midline

Heron’s formula

area = sqrt(s(s-a)(s-b)(s-c))

Unit circle

Closest to zero, sin is ½ and cos is sqrt(3)/2
Sin numerator gets bigger and cos gets smaller

(cos, sin)

cos 30

sqrt(3) / 2

cos 0

1

cos 45

sqrt(2) / 2

cos 60

1/2

cos 90

0

sin 0

0

sin 30

1/2

sin 45

sqrt(2) / 2

sin 60

sqrt(3)/2

sin 90

1

Sin / cos identity

sin²(θ) + cos²(θ) = 1

Tan identity

1 + tan²(θ) = sec²(θ)

Cot identity

1 + cot²(θ) = csc²(θ)