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Trigonometry Questions - All Grades

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Grade 12 Trigonometry

Tangent of

$30deg$ is equal to

$(sin 30deg)/(cot30deg)$ .

True
False

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.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.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.

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.C.8

A helicopter just took off from a landing pad. It travels straight up in the air for 35 m, and then travels forward, parallel to the ground for 85 m. If a person is standing where the helicopter took off from, what is the angle of elevation from that person to where the helicopter currently is? Round the answer to the nearest tenth of a degree.

22.4°
24.3°
65.7°
67.6°

Grade 10 Trigonometry

In a 45-45-90 triangle, the hypotenuse is the leg multiplied by .

2
the square root of 2
the natural logarithm of 2

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

Point M,

$(4/5, -3/5)$ , is on the unit circle centered at the origin. The angle

$theta$ is in standard position, with its terminal arm passing through point M. What is the value of

$tan(theta) ?$

$-3/5$
$4/5$
$-4/3$
$-3/4$

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

$Delta LMN$ ,

$LM = 7.5 \ "units"$ ,

$MN = 6 \ "units"$ , and

$m ang L = 49°$ . 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 10 Trigonometry CCSS: HSG-SRT.D.10

$AB=17$ ,

$ang C = 26deg$ , and

$AC= 6$ , what is value of

$ang B$ ?

$3.2 deg$
$.4 deg$
$1.2 deg$
$8.9 deg$

Grade 12 Trigonometry CCSS: HSF-TF.A.4

What is the period of the sine function?

$pi$
$2pi$
$1/2pi$
$4pi$

Grade 11 Trigonometry

The hypotenuse of a 30-60-90 triangle is 6. What is the length of the short leg?

$4sqrt2$
$4sqrt3$
3
12

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

For triangle ABC,

$cos(C) = 1/sqrt(2)$ . What is the value of

$BC$ if

$AC = sqrt(3) \ "units"?$

$sqrt(2) \ "units"$
$sqrt(3)/2 \ "units"$
$sqrt(6) \ "units"$
$1 \ "unit"$

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

The side lengths of triangle ABC are as follows:

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

$tan(B) ?$

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

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

Which of the following is an alternate form of the Pythagorean Identity? Choose all correct answers.

$tan^2(theta) + sin^2(theta) = 1$
$tan^2(theta) + 1 = sec^2(theta)$
$1 + sec^2(theta) = cot^2(theta)$
$1 + cot^2(theta) = csc^2(theta)$

Grade 12 Trigonometry CCSS: HSF-TF.A.4

The sine function is

even.
odd.
either.
neither.

Grade 11 Trigonometry

Using SOH CAH TOA, what does the first part, SOH, stand for?

sine=adjacent/hypotenuse
sine=hypotenuse/opposite
sine=opposite/adjacent
sine=opposite/hypotenuse

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

The side lengths of triangle ABC are as follows:

$AC = 4sqrt(3) \ "units", \ BC = 4 \ "units", \ AB = 8 \ "units"$ . What is the value of

$cos(A) ?$

$4/sqrt(3)$
$1/2$
$sqrt(3)/2$
$sqrt(3)/8$

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

Angle A is in standard position. It's terminal arm intersects the unit circle at

$(-3/10, sqrt(91)/10)$ . What is the value of

$cos(A) ?$

$-3/sqrt(91)$
$-sqrt(91)/3$
$sqrt(91)/10$
$-3/10$

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