Math 1060 Final Review

Solve triangle ABC. Round side lengths and angle measures to the nearest tenth when necessary. a = 20, b = 35, c = 42

A=28.3°, B=56°, C =95.7°

Write the vector v in the form v1i + v2j, given v, and the direction angle Ό of v. IIvII=15, Ό = 150°

-15sqr3/2i+15/2j

Find the amplitude, period, or phase shift of the given function as requested. Find the phase shift of y=5sin[6(x +pi/6)]

-pi/6

Use half-angle identities to find the exact value of the expression. sin 5pi/12

1/2sqr2+sqr3

Convert the angle from degrees to radians. Express the answer as a multiple of Δ. 570°

19pi/6

Use a sketch to find the exact value of y. y = sin(tan^-1 2)

2sqr5/5

Find the length of the arc on the circle of radius r meters intercepted by a central angle Ό. Round your answer to three decimal places. r = 5, Ό = 35°

3.054 m

Use the information given about the angle Ό, to find the exact value of the indicated trigonometric function. tan Ό = 7/24, Ό in quadrant III Find sin 2Ό.

336/625

Find the expression. u = <9, 6> Find IIuII

3sqr13

Find all solutions of the equation in the interval [0, 2Δ). 2 sin^2 Ό-3sin Ό - 2 = 0

7pi/6, 11pi/6

Find the area of triangle ABC (see the figure) with the given information. Round to the nearest tenth. B = 60.8°, a = 36.2 feet, c = 72.4 feet

K= 1143.9ft^2

Solve the SSA triangle. Indicate whether the given measurements result in no triangle, one triangle, or two triangles. Solve the resulting triangle. Round angle measures to the nearest degree and lengths to the nearest tenth when necessary. B = 41°, a = 4, b = 3

Solution 1: A = 61°, C = 78°, c = 4.5 Solution 2: A = 119°, C = 20°, c = 1.6

Solve triangle ABC. Round side lengths and angle measures to the nearest tenth when necessary. b = 7, c = 9, A = 125°

a=14.2, B=24°, C=31°

Find the amplitude, period, or phase shift of the given function as requested. Find the period of y = 2 sin[6(x + pi/2)] .

pi/3

Find all solutions of the equation. Express the solution in radians. sec x= sqr2

pi/4+ 2pin or 7pi/4 +2pin

Use trigonometric identities to solve each equation in the interval [0, 2Δ] 3 = 2 cos^2 x+ 3 sin x

pi/6, pi/2, 5pi/6

Find the exact values of the remaining trigonometric functions of Ό from the given information. cot Ό = - 24/7 , Ό in quadrant IV

sin Ό = - 7/25 cos Ό = 24/25 tan Ό = - 7/24 csc Ό = - 25/7 sec Ό = 25/24 cot Ό = - 24/7

Use the information given about the angle Ό to find the exact value of the indicated trigonometric function. sin Ό = 1/4, tan Ό > 0 Find cos Ό/2.

sqr8+2sqr15/4

Find a unit vector u in the direction of the given vector. <-12, -5>

<-12/13, -5/13>

Verify the identity 1 - cos^2x/1-sin x = - sin x

-sin x

Find the exact value of the expression. cos 165°

-sqr2-sqr6/4

Find the radian measure of a central angle of the circle of radius r that intercepts the arc of length s. Round your answer to three decimal places. r = 13.8 inches, s = 20 inches

1.449 radians

Find the area of the triangle by using Heron's formula. Round the answer to the nearest tenth. All sides are measured in inches. a = 40, b = 58, c = 67

1153.9 in^2

Solve triangle ABC. If necessary, round the answer to the nearest tenth. B = 21.2°, C = 105.6°, b = 17.5 centimeters

A = 53.2°, a = 38.7 cm, c = 46.6 cm