Trigonometry Study Guide 2026
Everything you need to pass the Trigonometry exam in one place: the exam format, every topic to study, real practice questions with explanations, flashcards, and full-length practice tests. Free, no sign-up needed.
📋 Trigonometry Exam Format at a Glance
📚 Trigonometry Topics to Study (55)
✍️ Sample Trigonometry Questions & Answers
1. In the unit circle, what are the coordinates of the point at 90∘?
On the unit circle, the coordinates (x, y) correspond to (cos θ, sin θ) for a given angle θ. At 90 degrees, the angle points directly along the positive y-axis. Therefore, the x-coordinate (cosine) is 0, and the y-coordinate (sine) is 1, resulting in the point (0,1).
2. What is the mode of: 2, 3, 3, 4, 5, 3, 6?
The mode is the value that appears most frequently. The number 3 appears three times, more than any other value.
3. Which identity correctly expresses cos(2θ) in terms of sin(θ) only?
The double-angle identity cos(2θ) = 1 − 2sin²(θ) is derived by substituting cos²θ = 1 − sin²θ into cos(2θ) = cos²θ − sin²θ.
4. Solve the equation 2sin(𝑥)cos(𝑥)= √3/2 for 0≤𝑥≤2𝜋.
The equation 2sin(x)cos(x) = √3/2 can be simplified using the double-angle identity for sine, which states that 2sin(x)cos(x) = sin(2x). So, the equation becomes sin(2x) = √3/2. Within the interval [0, 4π] for 2x (corresponding to [0, 2π] for x), the angles whose sine is √3/2 are π/3, 2π/3, 7π/3, and 8π/3. Dividing these by 2 gives the solutions for x as π/6, π/3, 7π/6, and 4π/3. Option D, x=π/3, 4π/3, correctly lists two of these valid solutions.
5. An airplane flying at 5,000 feet altitude begins its descent at a 3° glide slope angle. How far (horizontal distance) from the runway threshold should the descent begin?
Horizontal distance = 5000 / tan(3°) ≈ 5000 / 0.05241 ≈ 95,400 ≈ 95,500 feet.
6. What is the value of sin(π/4) · cos(π/4)?
sin(π/4) = cos(π/4) = √2/2, so their product is (√2/2)² = 2/4 = 1/2.