20 random questions | 15 minutes | Questions are randomized every attempt. Good luck!
Trigonometry Formulas
1 / 20
What is the Pythagorean identity involving cot and csc?
Pythagorean identity: 1 + cot²θ = csc²θ. Derived by dividing sin²θ + cos²θ = 1 by sin²θ.
2 / 20
How many degrees are in π radians?
π radians = 180°. So to convert radians to degrees multiply by 180/π.
3 / 20
What is sec(0°)?
sec(0°) = 1/cos(0°) = 1/1 = 1.
4 / 20
What is sin(180°)?
sin(180°) = 0. At 180° on the unit circle, the point is (-1,0), so y = 0.
5 / 20
What is the reference angle for 150°?
Reference angle for 150° = 180° - 150° = 30°. Reference angles are always acute (0° to 90°).
6 / 20
What is sin(30°)?
sin(30°) = 1/2. Key unit circle value to memorize: 30°=1/2, 45°=√2/2, 60°=√3/2.
7 / 20
What is tan(30°)?
tan(30°) = 1/√3 = √3/3 ≈ 0.577. Using sin(30°)/cos(30°) = (1/2)/(√3/2) = 1/√3.
8 / 20
What is cos(60°)?
cos(60°) = 1/2. Note: cos(60°) = sin(30°) = 1/2. Complementary angles share trig values.
9 / 20
What is tan(45°)?
tan(45°) = 1. Since sin(45°) = cos(45°) = √2/2, their ratio is 1.
10 / 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.
11 / 20
What is cos(30°)?
cos(30°) = √3/2. Note: cos(30°) = sin(60°) — complementary angles swap sin and cos.
12 / 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°].
13 / 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.
14 / 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.
15 / 20
What is sin(θ) equal to?
SOH: Sine = Opposite / Hypotenuse. Remember SOH-CAH-TOA!
16 / 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.
17 / 20
What does SOHCAHTOA stand for?
SOHCAHTOA: Sin=Opposite/Hypotenuse, Cos=Adjacent/Hypotenuse, Tan=Opposite/Adjacent.
18 / 20
What is the reference angle for 300°?
Reference angle for 300° = 360° - 300° = 60°. In Q4, subtract from 360°.
19 / 20
What is the Pythagorean identity involving tan and sec?
Pythagorean identity: 1 + tan²θ = sec²θ. Derived by dividing sin²θ + cos²θ = 1 by cos²θ.
20 / 20
What is the period of tan(x)?
The period of tan(x) is π (180°). It repeats every π radians.
Your score is
The average score is 0%
Restart quiz
🎯 Register FREE to save your score and unlock 1000+ more free quizzes!
👉 Register Now — It’s Free!
