Trigonometry Exam

In unit-hypotenuse triangle ABC with right angle C, what is the length of a and b?

a = sin A, b = cos A

If a, b, c is a Pythagorean triple, its unit-hypotenuse triangle will be ___.

a/c, b/c, 1

If two triangles have the same unit-hypotenuse triangle, they are ___.

similar

If measure of angle A + B = 90, then ___.

sin A = cos B

tan A =

(sin A)/(cos A)

Pythagorean Identity

(sin A)^2 + (cos A)^2 = 1

cos A and sin B in Quadrant I

\+, +

cos A and sin B in Quadrant II

\-, +

cos A and sin B in Quadrant III

\-, -

cos A and sin B in Quadrant IV

\+, -

cos A =

x-coordinate on a unit circle

sin A =

y-coordinate on a unit circle

An angle in ___ has its vertex at the origin and is the angle measured to the positive x-axis.

standard position

The reference angle is the ___.

positive acute angle made with the x-axis

csc A =

1/(sin A)

sec A =

1/(cos A)

cot A =

1/(tan A)

Coterminal angles are ___.

angles in standard position that have a common terminal side

Radian measure is the ___.

ratio of arc length s to radius r (A = s/r)

Radians =

((degrees A)/360)(2pi)

Degrees are ___ and are therefore ___.

based on observation; a posterior knowledge

Radians are ___ and are therefore ___.

based on calculation; a priori knowledge

360 degrees =

2pi radians

180 degrees =

pi radians

90 degrees =

pi/2 radians

270 degrees

3pi/2 radians

Radius = arc length → radians =

1

Sine: 5 points

P1: 0, P2: 1, P3: 0, P4: -1, P5: 0

Cosine: 5 points

P1: 1, P2: 0, P3: -1, P4: 0, P5: 1

Sine basic formula

a sin(k(x - d)) + b

Cosine basic formula

a cos(k(x - d)) + b

P =

2pi/k

a represents

amplitude → added/subtracted from midline

k represents

frequency → determines number of cycles that occur in one revolution of the circle

P represents

period → difference between x-coordinates over one cycle

d represents

phase shift → horizontal translation

b represents

vertical translation & midline

Amplitude

(a) half the vertical distance from the maximum to the minimum; also the distance from the maximum or minimum to the midline

Period

(2pi/k) the horizontal distance between two consecutive peaks or troughs

Midline

(b) an imaginary horizontal line representing the function’s average value (over a full period); also the function’s vertical shift (up if positive, down if negative)

Maximum

(b+a) the function’s greatest y-value

Minimum

(b-a) the function’s least y-value

Phase shift

(d) how far the function is shifted horizontally (left if negative, right if positive)