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Trigonometry Formulas
1 / 20
What is the formula for the area of a triangle using two sides and included angle?
Area = ½ab sinC, where a and b are two sides and C is the included angle between them.
2 / 20
What is the formula for the area of a triangle using the Law of Sines?
Area = ½ab sinC, where a and b are two sides and C is the included angle.
3 / 20
What is the angle addition formula for cos(A+B)?
cos(A+B) = cos(A)cos(B) - sin(A)sin(B). Note the minus sign — a common mistake is using plus.
4 / 20
What is sin(θ) equal to?
SOH: Sine = Opposite / Hypotenuse. Remember SOH-CAH-TOA!
5 / 20
What is the period of tan(x)?
The period of tan(x) is π (180°). It repeats every π radians.
6 / 20
What is the Law of Sines?
Law of Sines: a/sinA = b/sinB = c/sinC. Use when you have angle-side pairs.
7 / 20
What is the reference angle for 150°?
Reference angle for 150° = 180° - 150° = 30°. Reference angles are always acute (0° to 90°).
8 / 20
How do you convert degrees to radians?
Degrees to radians: multiply by π/180. Example: 90° × π/180 = π/2 radians.
9 / 20
What is the formula for cos(A-B)?
cos(A-B) = cos(A)cos(B) + sin(A)sin(B). Note the plus sign — different from cos(A+B).
10 / 20
What is the exact value of cos(45°)?
cos(45°) = √2/2 ≈ 0.707. In a 45-45-90 triangle, adjacent/hypotenuse = 1/√2 = √2/2.
11 / 20
What is tan(45°)?
tan(45°) = 1. Since sin(45°) = cos(45°) = √2/2, their ratio is 1.
12 / 20
What is the co-function identity for sin and cos?
Co-function identity: sin(θ) = cos(90°-θ). Complementary angles share trig values with paired functions.
13 / 20
What is the period of y = sin(Bx)?
Period = 2π/B. A larger B compresses the graph (shorter period); smaller B stretches it.
14 / 20
What is the inverse sine function sin⁻¹(x) used for?
sin⁻¹(x) (arcsin) gives the angle whose sine is x. Range is [-90°, 90°].
15 / 20
What is the range of the tangent function?
Range of tan(x) is all real numbers (-∞, +∞). It has no maximum or minimum.
16 / 20
What is tan(θ) equal to?
TOA: Tangent = Opposite / Adjacent. Also: tan(θ) = sin(θ)/cos(θ).
17 / 20
What is cos(θ) equal to?
CAH: Cosine = Adjacent / Hypotenuse. Remember SOH-CAH-TOA!
18 / 20
What is the inverse cosine cos⁻¹(x) also called?
cos⁻¹(x) is called arccosine (arccos). It gives the angle whose cosine is x. Range: [0°, 180°].
19 / 20
What is the formula for the angular velocity ω?
Angular velocity ω = θ/t, where θ is the angle in radians and t is time. Units: radians/second.
20 / 20
What is the formula for the angle subtraction identity sin(A-B)?
sin(A-B) = sin(A)cos(B) - cos(A)sin(B). Change the sign from the addition formula.
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