IM3- Chapter 9 Review

Using Trig Identities

100

Simplify. 

tan(pi/2-x)*sinx

cosx

200

Simplify. 

cos(theta)*sec(-theta)

1

300

Simplify. 

(csc^2x-cot^2x)/(cosx*tan(-x)

-cscx

400

Find the values of the other 5 trig functions. 

cos theta=5/6, (3pi)/2<theta<2pi

sintheta=-sqrt(11)/6,csctheta=-(6sqrt11)/11

costheta=5/6, sectheta=6/5

tantheta=-(sqrt(11))/5, cottheta=-(5sqrt(11))/11

500

Find the other five trig functions. 

csc theta=-5/3, pi<theta<(3pi)/2

sin theta=-3/5, csc theta=-5/3

cos theta=-4/5, sec theta=-5/4

tan theta=3/4, cot theta=4/3

Sum and Difference Formulas

100

Simplify the expression. 

cos(x-pi/2)

sin x

200

Simplify the expression. 

tan(x+pi)

tan x

300

Find the exact value of the expression 

sin((5pi)/12)

(sqrt2+sqrt6)/4

400

Solve the equation. 

sin(pi/4-x)-sin(pi/4+x)=1, 0<=x<2pi

x=(5pi)/4,(7pi)/4

500

Find tan(a - b) given the following:

sin a=8/17, pi/2<x<pi

cos b = -24/25, pi<b<(3pi)/2

-297/304

Law of Sines

100

Find the area of a triangle where A = 97^o, b = 25 and c = 19

235.7

200

Determine whether the measurements determine no triangle, 1 triangle, 2 triangles. 

A=49^o, a = 12, b = 18

No triangle

300

Solve for a given that C = 48^o, b = 20, c = 28. Round your answer to the nearest tenth.

37.1

400

Solve the triangle(s) given that A = 31^o, a = 10, b = 12. Round your answer to the nearest tenth.

Triangle 1: B=38.2, C = 110.8, c=18.2

Triangle 2: B=141.8, C=7.2, c=2.4

500

Solve the triangle(s) given that A = 57^o, B = 91^o, c = 45. Round your answer to the nearest tenth.

C=32, a=71.2, b=84.9

Law of Cosines

100

Find the area of triangle ABC with side lengths of 7ft, 12 ft, 15 ft to the nearest tenth.

41.2 ft²

200

Find the measure of angle B given that a = 9, b = 22, and c = 29. Round your answer to the nearest tenth.

B=33.0

300

Find the measure of angle A given that C = 57^o, a = 19, b = 29. Round your answer to the nearest tenth.

A = 40.5

400

Find all 3 angles of the triangle with sides of a = 22, b = 8, c = 15. Round your answers to the nearest tenth.

A=144.3, B=12.2, C=23.4

500

The distance from the Bermuda triangle to Miami, Florida is 1677 km. If you rotate 63^o , the distance from Bermuda Triangle to San Juan, Puerto Rico is 1553 km. What is the distance from Miami to San Juan?

1691.0 km

Solving Trig Equations

100

Find exact solutions over the interval 0 < x <2pi

2cosx-sqrt3=0

x=pi/6or(11pi)/6

200

Find exact solutions over the interval 0 < x <2pi

sin^2x=-sinx

x=0,pi,(3pi)/2

300

Find exact solutions over the interval 0 < x <2pi

sec(pi/2-x)*cscx=2

x=pi/4, (3pi)/4, (5pi)/4,(7pi)/4

400

Find exact solutions over the interval 0 < x <2pi

sqrt3-tanx=0

x=pi/3 or (4pi)/3

500

Find exact solutions over the interval 0 < x <2pi

2cos^2x+3sinx=0

x=(5pi)/6,(7pi)/6