Test 4 Jeopardy

Trigonometric Identities

100

an identity involving trigonometric functions

Trigonometric Identity

200

sin(θ)/cos(θ) + cos(θ)/(1+ sin(θ))

sec(θ)

300

Prove.

cos(θ)/1- sin(θ)= sec(θ) + tan(θ)   

correct

400

Prove.

1+cos(θ)/cos(θ) = tan²(θ)/sec(θ)-1  

sec(θ) + 1=sec(θ) + 1

500

Prove.

sec(x) + csc(x)/ tan(x) + cot(x)= cos(x)

No.

sin(x)=cos(x)

Addition & Subtraction Formulas

100

sin(s+t) = ?

sin(s)cos(t) + cos(s)sin(t)

200

cos(s-t) = ?

cos(s)cos(t) + sin(s)sin(t)

300

tan(s+t) = ?

tan(s)+tan(t)/1-tan(s)tan(t)

400

Solve.

sin 20° cos 40° + sin 40° cos 20°

sin 60°= √3/2

500

Evaluate sin(x+t), where sin(x)=12/13 with x in Quadrant II and tan(t)=3/4 with t in Quadrant III

-33/65

Double & Half Angle Formulas

100

Allow us to find the values of the trigonometric functions at 2x from their values at x

Double-Angle Formula

200

Relate the values of the trigonometric functions at 1/2x to their values at x

Half-Angle Formula

300

tan(2) = ?

2tan(x)/1-tan²(x)

400

Solve.

Sin(3x)/sin(x)cos(x)

4cos(x)- sec(x)

500

Find the exact value of sin 22.5°

(1/2)√ (2-√ 2)

Product-Sum Formulas

100

Relate products of sines and cosines to sums of sines and cosines

Product-Sum Formula

200

sin(u)cos(v) = ?

1/2[sin(u+v) + sin(u-v)]

300

sin(u)sin(v) = ?

1/2[cos(u-v) - cos(u+v)]

400

Write sin(7x) + sin(3x) as a product

2sin(5x)cos(2x)

500

Solve.

sin(3x)-sin(x) / cos(3x)+cos(x)

tan(x)

Trigonometric Equations

100

sin²(x)+cos²(x) = ?

1

200

Find the solution of one period.

cos(θ) = .65

θ is about .86, 5.42

300

sin(θ)=1/2

θ = π/6 + 2kπ and 5π/6 + 2kπ

400

2cos²θ - 7cosθ + 3 = 0

θ = π/3 + 2kπ  and 5π/3 + 2kπ

500

1 + sin(θ) = 2cos²(θ)

θ = π/6 + 2kπ and 5π/6 + 2kπ and 3π/3 + 2kπ