Trigonometry Flashcards

6 cards from real AMC12 practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 6 Trigonometry flashcards as text

In which quadrant is tan(θ) negative and sin(θ) positive?
Answer: II
In quadrant II, sin > 0 but cos < 0, making tan = sin/cos < 0.
What is the range of arcsin(x)?
Answer: [−π/2, π/2]
The arcsin function has range [−π/2, π/2] by convention as the principal value.
Which identity is correct?
Answer: 1 + tan²(θ) = sec²(θ)
Dividing sin²θ + cos²θ = 1 by cos²θ gives 1 + tan²θ = sec²θ.
What is the amplitude of y = 3cos(2x − π)?
Answer: 3
The amplitude of y = A cos(bx + c) is |A| = 3.
Using the law of sines in triangle ABC with A = 30°, a = 5, B = 90°, what is b?
Answer: 10
By the law of sines: 5/sin30° = b/sin90° → 10 = b.
If sin(θ) = √3/2, what is cos(2θ) using the identity cos(2θ) = 1 − 2sin²(θ)?
Answer: −1/2
cos(2θ) = 1 − 2(3/4) = 1 − 3/2 = −1/2.