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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 Law of Cosines?
Law of Cosines: c² = a² + b² - 2ab×cosC. Use when you don't have angle-side pairs.
3 / 20
What is sin(θ) equal to?
SOH: Sine = Opposite over Hypotenuse. Remember SOH-CAH-TOA!
4 / 20
What is sin(30°)?
sin(30°) = 1/2. Key unit circle value to memorize: 30°=1/2, 45°=√2/2, 60°=√3/2.
5 / 20
What is cos(0°)?
cos(0°) = 1. At 0°, the adjacent side equals the hypotenuse on the unit circle.
6 / 20
What is sin(60°)?
sin(60°) = √3/2 ≈ 0.866. Key unit circle value: sin(30°)=1/2, sin(45°)=√2/2, sin(60°)=√3/2.
7 / 20
What is the midline (vertical shift) in y = a sin(bx) + d?
The midline is y = d. The graph oscillates d units above and below this horizontal line.
8 / 20
What is sin(90°)?
sin(90°) = 1. At 90°, the opposite side equals the hypotenuse on the unit circle.
9 / 20
In which quadrant is sin positive but cos negative?
In Quadrant II (90°-180°), sin is positive and cos is negative. Remember: All Students Take Calculus (ASTC).
10 / 20
What is the period of tan(x)?
The period of tan(x) is π (180°). It repeats every π radians.
11 / 20
SOH: Sine = Opposite / Hypotenuse. Remember SOH-CAH-TOA!
12 / 20
What is tan(θ) equal to?
TOA: Tangent = Opposite / Adjacent. Also: tan(θ) = sin(θ)/cos(θ).
13 / 20
What is cos(θ) equal to?
CAH: Cosine = Adjacent / Hypotenuse. Remember SOH-CAH-TOA!
14 / 20
What is sec(0°)?
sec(0°) = 1/cos(0°) = 1/1 = 1.
15 / 20
What is the half-angle identity for cos²(θ)?
Power-reducing: cos²θ = (1 + cos2θ)/2.
16 / 20
What is the reference angle for 120°?
Reference angle for 120° = 180° - 120° = 60°. In Q2, subtract from 180°.
17 / 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°].
18 / 20
What is the phase shift in y = sin(x - c)?
Phase shift: y = sin(x-c) shifts RIGHT by c. y = sin(x+c) shifts LEFT by c.
19 / 20
What mnemonic helps remember which trig functions are positive in each quadrant?
ASTC (All Students Take Calculus): All positive in Q1, Sin in Q2, Tan in Q3, Cos in Q4.
20 / 20
What is tan(45°)?
tan(45°) = 1. Since sin(45°) = cos(45°) = √2/2, their ratio is 1.
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