Algebra and Trigonometry: The Unit Circle, Sine and Cosine Functions flashcards

Question 1

What is an angle, in terms of rays?

Accepted Answer

The union of two rays that share a common endpoint.

Question 2

What is the vertex of an angle?

Accepted Answer

The shared endpoint of the two rays forming the angle.

Question 3

When is an angle in standard position?

Accepted Answer

Its vertex sits at the origin and its initial side is on the positive x-axis.

Question 4

In which direction is a positive angle measured?

Accepted Answer

Counterclockwise from the positive x-axis.

Question 5

In which direction is a negative angle measured?

Accepted Answer

Clockwise from the positive x-axis.

Question 6

What is a degree, as a fraction of a full revolution?

Accepted Answer

One 360th of a full turn of a circle.

Question 7

What is one radian?

Accepted Answer

The central angle that intercepts an arc whose length equals the circle's radius.

Question 8

What are coterminal angles?

Accepted Answer

Angles in standard position that share the same terminal side.

Question 9

What do you add or subtract to find a coterminal angle?

Accepted Answer

360° (or 2π radians).

Question 10

What is a reference angle?

Accepted Answer

The acute angle between the terminal side of an angle and the horizontal axis.

Question 11

What is the formula for arc length s on a circle of radius r with central angle θ (radians)?

Accepted Answer

s = rθ

Question 12

What is the area of a sector with radius r and central angle θ (radians)?

Accepted Answer

A = (1/2)θr^2

Question 13

What is the hypotenuse of a right triangle?

Accepted Answer

The side across from the right angle.

Question 14

In a right triangle, what is sin t as a ratio of sides?

Accepted Answer

opposite / hypotenuse

Question 15

In a right triangle, what is tan t as a ratio of sides?

Accepted Answer

opposite / adjacent

Question 16

What is a unit circle?

Accepted Answer

A circle centered at (0, 0) with radius 1.

Question 17

On the unit circle, which coordinate of the point for angle t gives cos t?

Accepted Answer

The x-coordinate: cos t = x.

Question 18

On the unit circle, which coordinate of the point for angle t gives sin t?

Accepted Answer

The y-coordinate: sin t = y.

Question 19

What is the Pythagorean Identity?

Accepted Answer

cos^2 t + sin^2 t = 1

Question 20

What are the domain and range of sine and cosine?

Accepted Answer

Domain: all real numbers; range: [−1, 1].

Question 21

Of which function is secant the reciprocal?

Accepted Answer

Cosine: sec t = 1/cos t.

Question 22

Of which function is cosecant the reciprocal?

Accepted Answer

Sine: csc t = 1/sin t.

Question 23

How is tan t written using sine and cosine?

Accepted Answer

tan t = sin t / cos t

Question 24

What cofunction identity links sin t to cosine?

Accepted Answer

sin t = cos(π/2 − t)

Question 25

Which of the six trig functions are even?

Accepted Answer

Cosine and secant.

Question 26

When is a function f odd?

Accepted Answer

When f(−x) = −f(x) for every x in its domain.

Algebra and Trigonometry: The Unit Circle, Sine and Cosine Functions flashcards

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