Math-1113 Study Guide Final Part 2

Trigonometric Identities

100

( 1 - cos² x) ( 1 + cot² x) can be simplified to...

What is 1

200

Tan (theta) * Cos (theta) can be simplified to this simple trigonometric expression.

What is Sin(theta)

300

Tan (x) Sin (x) + sec (x) cos²(x) can be simplified to this simple trigonometric expression.

What is sec (x)

400

sec (x) + csc (x) / 1 + tan (x) can be simplified to this simple trigonometric expression.

What is csc (x)

500

1 + tan² (x) / csc² (x) + sin² (x) + 1 / sec² (x) can be simplified to this simple trigonometric expression.

What is sec² (x)

Sum and Difference Identities

100

The exact value of cos (pi /12)

What is sqrt(2) + sqrt(6) / 4

200

The exact value of tan (19pi / 12)

What is -2 - sqrt(3)

300

The expression: sin (x - (3pi / 4)) rewritten in terms of sin and cos

What is (-sqrt(2) / 2)sin(x) - (sqrt(2) / 2)cos(x)

400

The simplified form of sec (pi/2 - theta)

What is csc (theta)

500

The exact value of the expression: cos ( cos^-1 (sqrt(2) / 2) + sin^-1 (sqrt(3) / 2))

What is sqrt(2) - sqrt(6) / 4

Double, Half and Reduction Formulas

100

The exact value of sin (2x) given sin (x) = 1 / 8 and x is in quadrant I

What is 3sqrt(7) / 32

200

The exact value of cos (2x) given cos (x) = -1 / 2 and x is in quadrant III

What is -1 / 2

300

The simplified form of the expression: 2 sin (pi / 4) 2 cos (pi / 4)

What is 2 sin (pi / 2)

400

The exact value of sin (x / 2) given sin (x) = -12 / 13 and x is in quadrant III

What is 3sqrt(13) / 13

500

The exact value of cos (x / 2) given sec (x) = -4 and x is in quadrant II

What is sqrt(6) / 4

Trigonometric Equations

100

Every solution of 2 sin (theta) = sqrt(3) from 0 to 2pi

What are pi / 3 and 2pi / 3

200

Two solutions of 4 sin² (theta) - 2 = 0 from 0 to 2pi

What are pi / 4, 3pi / 4, 5pi / 4, or 7pi / 4

300

Every solution of 2 cos (theta) = -1 from 0 to 2pi

What are 7pi / 6 and 11pi / 6

400

Every solution of 2 cos² (x) + cos (x) = 1 from 0 to 2pi

What are pi / 3, pi, and 5pi / 3

500

Every solution of cos (2x) = sin(x) from 0 to 2pi

What are 3pi / 2, pi / 6, and 5pi / 6

Non-Right Triangles

100

The angle that corresponds to a side of 13 with another side measuring 6 with an angle of 20*

What is 47.8*

200

The area of a triangle with one side measuring 32 with another side measuring 24 with an angle of 75* being placed opposite to neither of those 2 sides.

What is 370.9

300

The side that corresponds to an angle of 120* with the other two sides measuring 6 and 7

What is 11.3

400

The angle that corresponds to a side of 13 with two other sides measuring 22 and 28

What is 26.9*

500

The area of a triangle with sides of length 18, 21, and 32

What is 177.56