Eleventh Grade (Grade 11) Trigonometry Questions for Tests and Worksheets

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Grade 11 Trigonometry CCSS: HSG-SRT.D.10

$Delta XYZ$ ,

$XY = 12 \ "units"$ ,

$YZ = 15 \ "units"$ , and

$m ang X = 50°$ . Using the law of sines and the given information, which of the following is true?

No such triangle exists.
These measurements result in a unique triangle.
These measurements result in two possible triangles.
The law of sines cannot be used in this situation.

Grade 11 Trigonometry

Simplify

$sin⁡ x \ csc⁡ x$ .

$sin ^2 x$
$-1$
$tan x$
$1$

Grade 11 Trigonometry CCSS: HSG-SRT.C.6

$Delta ABC$ ,

$AB = 2 \ "units"$ and

$AC = 5 \ "units"$ . What is the measure of angle C, rounded to one decimal place?

0.4°
21.8°
23.6°
68.2°

Grade 11 Trigonometry CCSS: HSF-TF.A.4

This question is a part of a group with common instructions. View group »

For this investigation of trigonometric functions and their symmetry, the unit circle was used (circle A). Why was the unit circle used, and not a circle with a different radius (not equal to one unit)?

Because the absolute value of the maximum and minimum values of the sine and cosine functions are 1.
The circumference of a circle is $C = 2 pi r$ . If the radius is not equal to 1, the circumference would be greater than or less than $2pi$ . Since the period of sine and cosine is $2pi$ , this would mean that the values of these functions on the circle would not fit.
It simplifies the math, allowing the coordinates of the points on the unit circle to be equal to the sine and cosine of angles in standard position.
There is no particular reason, it is simply convention to use the unit circle. All the math and reasoning would have been exactly the same using a circle centered at the origin with a different radius.

Grade 11 Trigonometry CCSS: HSG-SRT.C.6

If AC = 16, BC = 18, what is the measure of angle A?

48.4°
41.6°
27.3°
62.7°

Grade 11 Trigonometry CCSS: HSF-TF.B.5

What is the period of

$f(theta) = tan(3theta - 2) ?$

$pi/2$
$2/3$
$pi/3$
$(2pi)/3$

Grade 11 Trigonometry CCSS: HSF-TF.A.2

$-pi/3$ is equivalent to which of the following?

$(5pi)/6$
$(4pi)/3$
$pi/3$
$(5pi)/3$

Grade 11 Trigonometry CCSS: HSF-TF.A.2

Reference angles must be

in degrees.
positive and acute.
positive and obtuse.
in radians.

Grade 11 Trigonometry CCSS: HSF-TF.A.2

What is the reference angle for

$-115deg$ ?

55°
65°
235°
-35°

Grade 11 Trigonometry CCSS: HSG-SRT.D.10

$Delta QRS$ ,

$QR = 9 \ "units"$ ,

$RS = 6 \ "units"$ , and

$m ang R = 72°$ . Using the law of sines and the given information, which of the following is true?

No such triangle exists.
These measurements result in a unique triangle.
These measurements result in two possible triangles.
The law of sines cannot be used in this situation.

Grade 11 Trigonometry CCSS: HSG-SRT.C.7

$sin(85°)=cos(x)$ (assuming

$0°<= x <= 90°$ )

5°
15°
105°
85°

Grade 11 Trigonometry CCSS: HSG-SRT.C.6

The ratio of the largest leg of a right triangle to its hypotenuse will ALWAYS have the same value for ANY two similar right triangles.

True
False

Grade 11 Trigonometry CCSS: HSF-TF.A.2

Point P is a point on the unit circle centered at the origin whose coordinates are

$( (2sqrt(3))/5, -sqrt(13)/5)$ . The angle

$theta$ is the angle in standard form that has made between 4 and 5 full rotations around the origin, counterclockwise, and whose terminal arm intersects point P. What is the value of

$sin(theta) ?$

$sqrt(39)/6$
$(2sqrt(39))/13$
$(2sqrt(3))/5$
$-sqrt(13)/5$

Grade 11 Trigonometry

POSITIVE angles go in which direction?

clockwise
counter-clockwise
up
down

Grade 11 Trigonometry CCSS: HSF-TF.A.2

Which of the following is a coterminal angle for

$75deg$ ?

-135°
495°
315°
-285°

Grade 11 Trigonometry CCSS: HSG-SRT.D.11

A mountain, when viewed from a certain angle, appears to be a scalene triangle. The west side of the mountain makes an angle of elevation of 40°, the east side of the mountain makes an angle of elevation of 55°, and the base of the mountain is 3500 m wide. From this view, what is the direct distance from the base of the mountain at the east side to the top? Round the answer to the nearest meter.

2258 m
2746 m
2878 m
5424 m

Grade 11 Trigonometry CCSS: HSG-SRT.D.10

This question is a part of a group with common instructions. View group »

What is the missing reason in step 18?

Algebra (adding)
Pythagorean Identity
Pythagorean Theorem
Algebra (collect like terms)

Grade 11 Trigonometry CCSS: HSF-TF.A.1

$45deg$ and

$pi/6$ radians are equivalent angles.

True
False

Grade 11 Trigonometry

The reciprocal of

$sintheta$ is .

$1/(costheta)$
$1/(sectheta)$
$1/(cottheta)$
$1/(tantheta)$
none of these are correct

Grade 11 Trigonometry

$sin(theta)=24/25$ what is

$csc(theta)?$

$25/24$
$7/24$
$24/3$
$25/7$

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Eleventh Grade (Grade 11) Trigonometry Questions