Additional Topics on Analytic Trigonometry Review

Sum and Difference Formulas

100

Evaluate sin 19pi/12

(- sqrt 6 - sqrt 2 )/4

200

Evaluate cos 31pi/12

(sqrt 2 - sqrt 6) / 4

300

Evaluate tan 17pi/12

(sqrt 3) + 2

400

Suppose:

sin a = - 7 / 25, a in Q3

cos b = -4 / 5, b in Q3

Find cos(a - b)

117 / 125

Double Angle Formulas

200

sin x = -1/3, x in Q3

Find sin 2x

4 sqrt2 / 9 

300

sin x = 15/17, x lies in Q2

Find sin2x, cos2x, tan2x

-240 / 289

-161 / 289

240 / 161

Power Reducing Formulas

400

Use the power-reducing formulas to rewrite 

24 sin²x cos²x

3 - 3 cos 4x

500

Use the power-reducing formula to rewrite -12 sin ⁴ x

-9/2 + 6 cos 2x - 3/2 cos 4x

Half-Angle Formulas

100

Evaluate cos 22.5

sqrt(2 + sqrt2) / 2

200

Evaluate sin 15

sqrt(2 - sqrt3) / 2

300

Evaluate tan 3pi/8

sqrt2 + 1

Solve Trig Equations

200

Solve cos 2x - cos x = 0

x = 0

x = 2pi/3, 4pi/3

300

Solve sin²x = 2 sin² (x/2)

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

400

Solve 2 sin(x + pi/3) = tan pi/3

x = 0, pi/3, 5pi/3

500

Solve tan 2x + tan x = 0

x = 0, pi

x = pi/3, 2pi/3, 4pi/3, 5pi/3