algebra 2b - unit 3: trigonometry

what is the cosine of the angle?

cos(o) = -√3/2

what is the cosine of the angle? (1/2, -√3/2)

cos(o) = 1/2

which point forms a terminal side with the origin that creates an angle with a sine of √2/2 and a cosine of √2/2?

d

the length of the ___ equals the vertical distance from the point on the circle to the x-axis, which is the y-value of the point. the sine of an angle equals the ___/hypotenuse, and in the unit circle, the hypotenuse is always 1. the y-value divided by 1 equals the y-value.

opposite leg

which angle is 𝝅 radians?

positive angle ace

which angle is 3𝝅/2 radians?

positive angle acf

a segment drawn from the center of the circle to which letter creates a terminal side that forms a central angle of 𝝅/2 radians?

f

use reference angles to find the sine, cosine, and tangent of 210°.

sin(120°) = -1/2 cos(120°) = -√3/2 tan(120°) = √3/3

what is the tangent of the angle?

tan(o) = -1

what is the measure of an angle in standard position that has a terminal side from the origin to point i?

5pi/6

what is the measure of a 75° angle in radians?

5𝝅/12

match the blanks to their missing phrases to complete the proof.

blank a : r = 1 blank b : definition of sine black c : substitution

what is the measure of an angle in standard position that has a terminal side from the origin to point e?

pi/3

which angles are coterminal with a 95° angle? select all that apply.

815°, -265°, 1175°

use reference angles to find the sine, cosine, and tangent of 45°.

sin(45°) = √2/2 cos(45°) = √2/2 tan(45°) = 1

what is the sine of the angle?

sin(o) = -√3/2

https://cdstools.flipswitch.com/asset/media/1239204 what is the sine of 45 angle a?

√2/2

what is the sine of the 45 angle a?

√2/2

which angles are coterminal with a 30° angle? select all that apply.

-330°, 390°, 750°

https://cdstools.flipswitch.com/asset/media/1239206 what is the tangent of the 45 angle a?

1

lesson 13

radian measure

what is the sine of the angle? (-√3/2, 1/2)

sin(o) = 1/2

lesson 15

the pythagorean identity

examine the triangle. https://cdstools.flipswitch.com/asset/media/1239214 what is the sine of the 30 angle and the sine of the 60 angle?

the sine of the 30 angle is 1/2. the sine of the 60 angle is √3/2

from previous question, what is tan(o)?

-24/7

exam 1

100%

if an angle measures 5π/8 radians, what is the measure in degrees?

112.5

angle (o) has a terminal side located in quadrant iii of the coordinate plane and cos(o) = -4/5. what is tan(o)?

3/4

which points forms a terminal side with the origin that creates an angle with a sine of -√2/2 and a cosine of -√2/2?

L

what mistake did yelenia make, if any?

in step 4, she used the incorrect definition of sine.

the length of the ____ equals the horizontal distance from the origin to the point on the circle, which is the x-value of the point. the cosine of an angle equals the ____/hypotenuse, and in the unit circle, the hypotenuse is always 1. the x-value divided by 1 equals the x-value.

adjacent leg

which statement correctly describes the radian measure of positive angle ace?

it takes 2π radians to complete a circle. since ∠ace is 1/2 of the circle, ∠ace = π radians.

what are the lengths of sides a and b?

a. 6 ft. b. 6√3

examine the triangle. https://cdstools.flipswitch.com/asset/media/1239215 what is cosine of the 30 angle and the cosine of the 60 angle?

the cosine of the 30 angle is √3/2 the cosine of the 60 angle is 1/2

how many radians is positive angle acd?

𝝅/2

what is the measure of a 135° angle in radians?

3𝝅/4

what is the sine of the 30 angle and the sine of the 60 angle?

the sine of the 30 angle is 1/2. the sine of the 60 angle is √3/2

which statement correctly describes the radian measure of positive angle acb?

it takes 2𝝅 radians to complete a circle. since angle acb is 1/8 of the circle, angle acb = 𝝅/4 radians.

if o equals 45°, what is the measure of arc ab in radians?

𝝅/4

on the unit circle, in standard position, an angle of which measure is coterminal with an angle that measures 2𝝅/3 radians?

-4𝝅/3

angle (o) has a terminal side located in quadrant ii of the coordinate plane and sin(o) = 24/25. what is cos(o)?

-7/25

examine the triangle. https://cdstools.flipswitch.com/asset/media/1239216 what is the tangent of the 30 angle and the tangent of the 60 angle?

the tangent of the 60 angle is √3 the tangent of the 30 angle is √3/3

which points forms a terminal side with the origin that creates an angle with a sine of 1 and a cosine of 0?

f

lesson 12

special right triangles

on the unit circle, in standard position, an angle of which measure is coterminal with an angle that measures in π radians?

3π

if an angle measures 2𝝅/9 radians, what is the measure in degrees?

40°

what is the measure of a 105° angle in radians?

7𝝅/12

use reference angles to find the sine, cosine, and tangent of 120°.

sin(120°) = √3/2 cos(120°) = -1/2 tan(120°) = -√3

use reference angles to find the sine, cosine, and tangent of 135°.

sin(135°) = √2/2 cos(135°) = -√2/2 tan(135°) = -1

use reference angles to find the sine, cosine, and tangent of 330°.

sin(330°) = -1/2 cos(330°) = √3/2 tan(330°) = -√3/3

use reference angles to find the sine, cosine, and tangent of 225.

sine(225) = -√2/2 cosine(225) = -√2/2 tangent(225) = 1

what is the cosine of the 30 angle and the cosine of the 60 angle?

the cosine of the 60 angle is 1/2 the cosine of the 30 angle is √3/2

lesson 14

the unit circle

if an angle measures 5𝝅/4 radians, what is the measure in degrees?

225°

angle o has a terminal side located in quadrant iv of the coordinate plane and sin(o) = -8/17. what is tan(o)?

-8/15

angle o has a terminal side located in quadrant iv of the coordinate plane and sin(o) = -8/17. what is cos(o)?

15/17

if an angle measures 6𝝅/5 radians, what is the measure in degrees?

216°

on the unit circle, in standard position, an angle of which measure is coterminal with an angle that measures 3𝝅/5 radians?

23𝝅/5

if o equals 120°, what is the measure of arc ad in radians?

2𝝅/3

which angles are coterminal with a 140° angle? select all that apply.

500°, 580°

on the unit circle, in standard position, an angle of which measure is coterminal with an angle that measures 𝝅/4 radians?

9𝝅/4

match the blanks to their missing phrases to complete the proof.

blank a: a^2 + b^2 = c^2 blank b: definition of unit circle blank c: sin(o) = y/1 = y

examine the triangle. https://cdstools.flipswitch.com/asset/media/1239212 what are the lengths of sides a and b?

a = 1/2 cm b = √3/2 cm

examine the triangle. https://cdstools.flipswitch.com/asset/media/1239217 what are the lengths of sides a and b?

a = 3√2/2 ft. b = 3√2/2 ft.

examine the triangle. https://cdstools.flipswitch.com/asset/media/1239220 what are the lengths of sides a and c?

a = 4 mm c = 8 mm

examine the triangle. https://cdstools.flipswitch.com/asset/media/1239201 what are the lengths of sides a and b?

a = 5 ft b = 5ft

examine the triangle. https://cdstools.flipswitch.com/asset/media/1239211 what are the lengths of sides a and b?

a = 8√3 in. b = 8 in.

examine the triangle. https://cdstools.flipswitch.com/asset/media/1239203 what are the lengths of a and b?

a = √2/2 m b = √2/2 m

examine the triangle. https://cdstools.flipswitch.com/asset/media/1239203 what are the lengths of sides a and b?

a = √2/2 m b = √2/2 m

examine the triangle. https://cdstools.flipswitch.com/asset/media/1239219 what are the lengths of sides a and b?

a = √3/2 mi. b = 1/2 mi.

which point forms a terminal side with the origin that creates an angle with a sine of 1/2 and a cosine of √3/2?

b

examine the triangle. https://cdstools.flipswitch.com/asset/media/1239202 what are the lengths of b and c?

b = 3 in. c = 3√2 in.

examine the triangle. https://cdstools.flipswitch.com/asset/media/1239213 what are the lengths of sides b and c?

b = 7 ft. c = 14 ft.

a segment drawn from the center of the circle to which letter creates a terminal side that forms a central angle of 2𝝅/3 radians?

g

which image shows the correct ratios for a 45-45-90 triangle that can be used as a formula to figure out the missing side lengths?

https://cdstools.flipswitch.com/asset/media/1239197

which image shows the correct ratios for a 30-60-90 triangle that can be used as a formula to figure out the missing side lengths?

https://cdstools.flipswitch.com/asset/media/1239207

which statement correctly describes the radian measure of positive angle acf?

it takes 2𝝅 radians to complete a circle. since angle acf is 3/4 of the circle, angle acf = 3𝝅/4 radians.

a segment drawn from the center of the circle to which letter creates a terminal side that forms a central angle of 𝝅 radians?

j

which point forms a terminal side with the origin that creates an angle with a sine of 0 and a cosine of -1?

j

examine the triangle. https://cdstools.flipswitch.com/asset/media/1239218 which statements are true about angle b in this triangle? select all that apply.

the sine of b is √2/2 the tangent of b is 1

examine the triangle. https://cdstools.flipswitch.com/asset/media/1239221 which statements are true regarding the trigonometric ratios of this triangle? select all that apply.

the sine of the 60 angle is √3/2 the sine of the 30 angle is 1/2. the cosine of the 30 angle is √3/ 2 the cosine of the 60 angle is 1/2

examine the triangle. https://cdstools.flipswitch.com/asset/media/1239222 what is the tangent of the 30∘ angle and the tangent of the 60∘ angle?

the tangent of the 60 angle is √3 the tangent of the 30 angle is √3/3

what is the best critique of thomas's proof?

thomas should not have chosen pi/4 as the angle measurement. an identity needs to be proven true for all values of the variables involved. he correctly related sine and cosine to the legs of the right triangle and 1 to the hypotenuse.

https://cdstools.flipswitch.com/asset/media/1239205 what is the cosine of the 45 angle a?

√2/2