20 random questions | 15 minutes | Questions are randomized every attempt. Good luck!
Trigonometry Formulas
1 / 20
What is sin(θ) equal to?
SOH: Sine = Opposite / Hypotenuse. Remember SOH-CAH-TOA!
2 / 20
What is the formula for converting angular speed (radians/sec) to linear speed?
Linear speed v = ω × r, where ω is angular speed in radians/sec and r is the radius.
3 / 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°].
4 / 20
What does SOHCAHTOA stand for?
SOHCAHTOA: Sin=Opposite/Hypotenuse, Cos=Adjacent/Hypotenuse, Tan=Opposite/Adjacent.
5 / 20
What is the period of sin(x) and cos(x)?
The period of sin(x) and cos(x) is 2π (360°). One complete cycle takes 2π radians.
6 / 20
What is the reciprocal of sine?
Cosecant (csc) = 1/sin(θ). The reciprocals: csc=1/sin, sec=1/cos, cot=1/tan.
7 / 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.
8 / 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.
9 / 20
What is the formula for the half-angle identity sin²(θ)?
Half-angle/power-reducing: sin²θ = (1 - cos2θ)/2. Useful for integrating and simplifying.
10 / 20
What is tan(60°)?
tan(60°) = √3 ≈ 1.732. Using sin(60°)/cos(60°) = (√3/2)/(1/2) = √3.
11 / 20
What is the range of the tangent function?
Range of tan(x) is all real numbers (-∞, +∞). It has no maximum or minimum.
12 / 20
What is the formula for tan in terms of sin and cos?
tan θ = sin θ / cos θ. This is a fundamental quotient identity.
13 / 20
What is the graph of y = sin(x) called?
y = sin(x) produces a sinusoidal wave oscillating between -1 and +1 with period 2π.
14 / 20
What is sin(270°)?
sin(270°) = -1. At 270° on the unit circle, the point is (0,-1), so y = -1.
15 / 20
What is sec(0°)?
sec(0°) = 1/cos(0°) = 1/1 = 1.
16 / 20
What is the range of the sine function?
Range of sin(x) = [-1, 1]. The output oscillates between -1 and 1 for any input.
17 / 20
What is cos(180°)?
cos(180°) = -1. At 180° on the unit circle, the point is (-1,0), so x = -1.
18 / 20
What is sin(30°)?
sin(30°) = 1/2. Key unit circle value to memorize: 30°=1/2, 45°=√2/2, 60°=√3/2.
19 / 20
What is the inverse tangent tan⁻¹(x) also called?
tan⁻¹(x) is called arctangent (arctan). It gives the angle whose tangent is x. Range: (-90°, 90°).
20 / 20
In which quadrant are both sin and cos negative?
In Quadrant III (180°-270°), both sin and cos are negative. Only tan is positive there.
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