AP PreCalculus Flashcards: Sine and Cosine Function Values
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 10 cards to help you master important concepts.
Why are special triangles (like isosceles right and equilateral) useful for finding trigonometric function values?
They provide known, exact side-length ratios for specific angles (multiples of π/4 and π/6), allowing for the calculation of exact sine and cosine values without a calculator.
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Why are special triangles (like isosceles right and equilateral) useful for finding trigonometric function values?
They provide known, exact side-length ratios for specific angles (multiples of π/4 and π/6), allowing for the calculation of exact sine and cosine values without a calculator.
What is the primary objective when determining the coordinates of points on a circle centered at the origin using trigonometry?
The objective is to use the circle's radius (r) and the angle (θ) in standard position to find the specific (x, y) coordinates on the circle's circumference.
What special geometric shapes can be used to find exact values for sine and cosine of angles that are multiples of π/4 and π/6?
The geometry of isosceles right triangles (for π/4 multiples) and equilateral triangles (which create 30-60-90 triangles for π/6 multiples) can be used.
For a point (x, y) on a circle of radius r at angle θ, which trigonometric function defines the x-coordinate?
The cosine function defines the x-coordinate, as the full coordinate is (r cos θ, r sin θ).
What formula gives the coordinates of a point P where an angle θ's terminal ray intersects a circle of radius r centered at the origin?
The coordinates of point P are given by the formula (r cos θ, r sin θ).
How is the coordinate (x, y) of a point on a circle related to sine and cosine?
The x-coordinate is proportional to the cosine of the angle (x = r cos θ), and the y-coordinate is proportional to the sine of the angle (y = r sin θ).
To find the exact value of cos(π/6), the geometry of which special triangle would be used?
The geometry of an equilateral triangle, which can be split into two 30-60-90 right triangles, would be used.
For a point (x, y) on a circle of radius r at angle θ, which trigonometric function defines the y-coordinate?
The sine function defines the y-coordinate, as the full coordinate is (r cos θ, r sin θ).
A point is on a circle with a radius of 7, at an angle of θ. What are its coordinates in terms of cosine and sine?
The coordinates of the point are (7 cos θ, 7 sin θ).
To find the exact value of sin(π/4), the geometry of which special triangle would be used?
The geometry of an isosceles right triangle (a 45-45-90 triangle) would be used to find the exact value for sin(π/4).