TRIGONOMETRY QUIZ Practice

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. θ = π/6 radians, A = 62 square meters, r = ?

• 64.93 m

• 16.23 m

• 4.03 m

• 15.39 m

Tags

CCSS.HSG.C.B.5

Refer to the given right triangle with sides 7 and 9. Find cos θ.

Tags

CCSS.HSG.SRT.C.6

Refer to the given right triangle with sides 8 and 5. Find tan θ.

Tags

CCSS.HSG.SRT.C.6

Find the length s. Round the answer to three decimal places.

• 6.283 ft

• 1.571 ft

• 3.142 ft

• 2.546 ft

Tags

CCSS.HSG.C.B.5

Find the length of the intercepted arc given the angle measure and radius.

• 18.75π km or approximately 58.9 km

• 12.5π km or approximately 39.3 km

• 25π km or approximately 78.5 km

• 9.5π km or approximately 29.8 km

Tags

CCSS.HSG.C.B.5

Find the area of the sector with a central angle of 215° and a radius of 4.5 yd.

Tags

CCSS.HSG.C.B.5

Find the radian measure of the central angle of the circle of radius 6 centimeters that intercepts an arc of length 32 centimeters.

• θ = 16/3

• θ = 2/3

• θ = 3/16

• θ = 32/7

• θ = 6/5

Answer explanation

To find the central angle θ in radians, use the formula θ = arc length / radius. Here, θ = 32 cm / 6 cm = 16/3 radians. Thus, the correct answer is θ = 16/3.

Tags

CCSS.HSG.C.B.5

Find the value of the trig function indicated. csc θ [Right triangle with sides 3√5 (adjacent), 9 (hypotenuse), and θ as the angle] Fill in the blank: csc θ = _______

• csc θ = 3/2

• csc θ = 3√5

• csc θ = 9

• csc θ = 1/3

Answer explanation

In a right triangle, csc θ = hypotenuse / opposite. Here, the hypotenuse is 9 and the opposite side (not given) can be found using Pythagorean theorem. The opposite side is 3, so csc θ = 9/3 = 3.

Tags

CCSS.HSF.TF.A.2

Answer explanation

The area of a sector is given by A = (θ/2π) * r². Here, θ = 11π/6 and r = 2. Thus, A = (11π/6)/(2π) * 4 = 11/3 m². The correct answer is A = \frac{11\pi}{3} m².

Tags

CCSS.HSG.C.B.5

Find the value of the tangent for ∠A. (Triangle with sides AB = 12, AC = 8, right angle at C)

• (2√5)/2

• (√5)/2

• 2/3

• (√5)/3

Tags

CCSS.HSG.SRT.C.6