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

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Grade 11 Trigonometry

Which of the following is equal to Cos(186)?

Cos(6)
Cos(94)
Cos(174)
-Cos(94)

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

For any circle, the measure of a central angle which is subtended by an arc of equal length to the radius of that circle will ALWAYS be 1 radian.

True
False

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

A circular pathway is created with a diameter of 20 feet. If the pathway makes an arc of

$210deg$ how long is the pathway?

$210 \ "ft"$
$(7pi)/6$
$(35pi)/3 \ "ft"$
$35 \ "ft"$

Grade 11 Trigonometry

In a 30-60-90 triangle, the short leg measures 8 cm. What is the length of the hypotenuse?

$16sqrt3 \ "cm"$
$24 \ "cm"$
$8sqrt2 \ "cm"$
$16 \ "cm"$

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

$sin(34°)+ cos (90°)=sin(x)$ (assuming

$0°<= x <= 90°$ )

10°
56°
124°
34°

Grade 11 Trigonometry

Using SOH CAH TOA, what does TOA stand for?

tangent=opposite/hypotenuse
tangent=opposite/adjacent
tangent=adjacent/hypotenuse
tangent=adjacent/opposite

Grade 11 Trigonometry

Simplify.

$-5(cot^2 x - csc^2 x)$

$5$
$-5$
$-5 csc^2 x$
$5 sec ^2 x$

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

What is the exact value of

$tan(75°) ?$

$-2+sqrt(3)$
$2+sqrt(3)$
$1$
$2-sqrt(3)$

Grade 11 Trigonometry CCSS: HSF-TF.B.6

Which of the following best explains why the domain of a trigonometric function needs to be restricted in order for the inverse to be a function?

Trigonometric functions are periodic, meaning that there are multiple input values for a single output value. Therefore, for any inverse trigonometric function there will be multiple output values for a given input value.
The domain of trigonometric functions is all real numbers, or all real numbers with some exceptions as in the case of the tangent function. This will necessarily lead to issues with the inverse, since there are infinite input values.
The range of trigonometric functions is usually restricted to the values between -1 and 1. Therefore the domain must be restricted as well.
Trigonometric functions are based on the ratio of the sides of right triangles. As such, in order to ensure that the inverse function can also be applied to these ratios, the input of trigonometric functions must be restricted to an interval less than $pi$ , such as $-pi/2 < theta < pi/2$ .

Grade 11 Trigonometry CCSS: HSF-TF.B.6

What is the standard domain restriction for

$f(x) = sin(x)$ , in order to ensure that its inverse is a function?

$0 <= x <= pi$
$(-3pi)/2 <= x <= (-pi)/2$
$(-pi)/2 <= x <= pi/2$
$-pi <= x <= 0$

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

Which function's graph has a period of 8 and reaches a maximum height of 1 if at least one full period is graphed?

$y=-4cos(pi/4x)-3$
$y=-4cos(8x)-3$
$y=-4cos(pi/4x)+5$
$y=-4cos(8x)+5$

Grade 11 Trigonometry

The radius of the unit circle is

$pi$ units.

True
False

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

$Delta DEF$ ,

$DE = 5 \ "units"$ ,

$EF = 6 \ "units"$ , and

$m ang D = 22°$ . What is the length of

$bar{DF}$ , rounded to one decimal place? There may be more than one correct answer.

5.0 units
7.2 units
10.3 units
12.0 units

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

$Delta ABC$ ,

$AB = 29 \ "units", \ AC = 25 \ "units"$ , and

$BC = 5 \ "units"$ . What is the measure of

$ang C$ , rounded to one decimal place?

6.4°
33.8°
139.8°
164.6°

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

What is the midline of

$f(x) = 3cos(2x-1/3)-3 ?$

$y=3$
$y=0$
$y=-3$
$y=-1$

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

What is the amplitude of

$f(x) = 1/2 cos(pix-1)+2 ?$

$3/2$
$1/2$
$1$
$5/2$

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

What is the amplitude of

$f(x) = 4cos(pi/4x - pi) -4 ?$

$4$
$1$
$0$
$1/4$

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

In a right triangle, the two non-right angles are ALWAYS complementary.

True
False

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

What is the reference angle for

$(7 pi) /4 ?$

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

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

What reference angle would be used to calculate the trig function values for

$120deg$ ?

$0deg$
$30deg$
$45deg$
$60deg$
$90deg$

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Eleventh Grade (Grade 11) Trigonometry Questions