AP Precalculus - Trigonometry Exam

sin(A + B)

(sinAcosB) + (sinBcosA)

sin(A - B)

(sinAcosB) - (sinBcosA)

sin(A + B)

(sinAcosB) + (sinBcosA)

sin(A - B)

(sinAcosB) - (sinBcosA)

cos(A + B)

(cosAcosB) - (sinAsinB)

cos(A - B)

(cosAcosB) + (sinAsinB)

tan(A + B)

(tanA + tanB)/(1 - tanAtanB)

tan(A - B)

(tanA - tanB)/(1 + tanAtanB)

If a compass is bearing N60E, what’s another way of saying that?

E30N

Law of Sines ASA AAS

(sinA/a) = (sinB/b) = (sinC/c)

Law of Cosines SSS SAS

a² = b² + c² - 2bc*cosA
cosA = (b² + c² - a²)/2bc

What graph is this?

Inverse Sin Graph

What graph is this?

Inverse Cos Graph

What graph is this?

Inverse Tan Graph

What is the domain for the Inverse Sin Graph? Range?

-1 ≤ x ≤ 1

-π/2 ≤ y ≤ π/2

What is the domain for the Inverse Cos Graph? Range?

-1 ≤ x ≤ 1

0 ≤ y ≤ π

What is the domain for the Inverse Tan Graph? Range?

-∞ ≥ x ≥ ∞

-π/2 < y < π/2

sin2x

2sinxcosx

cos2x

cos²x - sin²x

1 - 2sin²x

2cos²x + 1

tan2x

2tanx / (1-tan²x)

Pythagorean Theorem for Trig Identities (3)

sin²θ + cos²θ = 1

1 + cot²θ = csc²θ

tan²θ + 1 = sec²θ

sin(3θ)

cos(3θ)

tan(3θ)

3sinθ - 4sin³θ

4cos³θ - 3cosθ

(3tanθ - tan³θ) / (1 - 3tan²θ)

sin(θ/2)

+-rad(1-cosθ/2)

cos(θ/2)

+-rad(1+cosθ/2)

tan(θ/2)

sinθ/(1+cosθ)

Area of Oblique Triangle SAS

½bc*sinA

Area of Triangles SSS

√[s(s-a)(s-b)(s-c)] [s=(a+b+c)/2]