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

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

Angle

$theta$ is the angle in standard position whose terminal arm intersects the unit circle (centered at the origin) at the point

$(7/12, sqrt(95)/12)$ . What is the value of

$sin(theta) ?$

$sqrt(95)/12$
$7/12$
$7/sqrt(95)$
$sqrt(95)/7$

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

Choose the function that has a period of

$3pi$ , an amplitude of

$4$ , and a midline of

$y = 1$ .

$f(x) = 4sin(2/3 x) + 1$
$f(x) = 4sin(3pi x) + 1$
$f(x) = 2sin(3pi x) + 2$
$f(x) = 2sin(2/3 x) + 2$

Grade 11 Trigonometry CCSS: HSG-SRT.C.8

Mark is about to go on a zipline for the first time. The zipline is simply a wire, attached high up in a tree at one end and to the ground at the other. Mark will climb the tree, have the harness he's wearing connected to the wire of the zipline, and then slide down the wire. If the wire is 27 m long, and the angle of elevation of the wire is 33°, how high up in the tree is the other end? Round the answer to the nearest tenth of a meter.

14.7 m
22.6 m
32.2 m
49.6 m

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

$Delta ABC$ , which of the following is/are equal to

$(AB)/(BC) ?$ There may be more than one correct answer.

$sin(B)$
$sin(C)$
$cos(B)$
$cos(C)$

Grade 11 Trigonometry CCSS: HSF-TF.C.9

What is the exact value of

$sin(345°) ?$

$1/2(sqrt(2)-1)$
$-1/4 (sqrt(2)+sqrt(6))$
$1/4(sqrt(6) - sqrt(2))$
$1/4(sqrt(2) - sqrt(6))$

Grade 11 Trigonometry CCSS: HSF-TF.C.8

$tan(theta) = sqrt(11)/11$ and

$pi < theta < (3pi)/2$ , what is the value of

$sec(theta) ?$

$-(2sqrt(33))/11$
$sqrt(110)/11$
$(2sqrt(33))/11$
$-sqrt(110)/11$

Grade 11 Trigonometry CCSS: HSF-TF.B.7

For

$-pi/2 <= theta <= pi/2$ , solve

$sin(theta) = sqrt(2)/2$ .

$-pi/4$
$pi/4$
$(3pi)/4$
$pi/3$

Grade 11 Trigonometry CCSS: HSF-TF.B.7

Solve

$tan(theta) = 1$ on the interval

$(-pi/2, pi/2)$ .

$pi/3$
$pi/2$
$pi/4$
$-pi/4$

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

Which of the following is true concerning the law of sines and right triangles?

The law of sines is not valid for right triangles.
The law of sines can only be proved for the acute angles of a right triangle.
The law of sines can be easily proved for a right triangle, using trig ratios and the fact that $sin(90°)=1$ .
The law of sines can proved for a right triangle, and the easiest proof involves the use of the Pythagorean Theorem and the formula for the area of a triangle.

Grade 11 Trigonometry CCSS: HSF-TF.A.3

The side lengths of

$Delta ABC$ are

$AB = 1 \ "unit", \ AC = sqrt(3) \ "units", BC = 2 \ "units"$ . What is the value of

$sin(C) ?$

$1/2$
$sqrt(3)/2$
$1/sqrt(3)$
$sqrt(3)$

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

$sin(45°)- cos (45°)=cos(x)$ (assuming

$0°<=x<=90°$ )

90°
0°
45°
22.5°

Grade 11 Trigonometry CCSS: HSF-TF.C.9

What is the exact value of

$tan(255°) ?$

$-2-sqrt(3)$
$-2+sqrt(3)$
$2-sqrt(3)$
$2+sqrt(3)$

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

An arc length of 2.62 m on a circle with a radius of 1 m would subtend an arc angle of how many radians?

$pi/2$
$(5pi)/3$
$(5pi)/6$
$(7pi)/6$

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

$Delta ABC$ is an acute triangle. The sine of angle A can be expressed as

$(BC)/(AC)$ .

True
False

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

In trapezoid ABCD,

$AB = 3.8 \ "mm"$ ,

$BC = 3 \ "mm"$ ,

$CD = 4.5 \ "mm"$ , and

$AD = 7.7 \ "mm"$ . If

$ang ABC$ and

$ang CDA$ are supplementary, what is the measure of

$ang ABC$ , rounded to the nearest tenth of a degree?

127.5°
134.0°
167.6°
Not enough information.

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 16?

Algebra (addition)
Quadratic Formula
Substitution Property of Equality
Distributive Property

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

Right triangles are NEVER obtuse.

True
False

Grade 11 Trigonometry CCSS: HSF-TF.C.9

What is the exact value of

$cos(105°) ?$

$(sqrt(2)-sqrt(6))/4$
$-(sqrt(2)+sqrt(6))/4$
$-1/2 + sqrt(6)/4$
$(sqrt(6)-sqrt(2))/4$

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

John needs to fell a tree but needs to know how tall it is. The tree makes an angle of 80 degrees with the ground. John walks 30 m in the direction the tree is leaning. From here he sights the top of the tree and finds the angle of inclination to be 30 degrees. What is the height of the tree?

10 m
21 m
16 m
15 m

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

In triangle

$ABC$ ,

$BC = 15 \ "in.", \ AB = 10 \ "in.",$ and

$m ang A = 100°$ . Find

$AC.$ Round the answer to one decimal place. The diagram is not to scale.

13.1 in.
10.3 in.
9.6 in.
11.2 in.

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Eleventh Grade (Grade 11) Trigonometry Questions