Solving Trig Equations

Solving Trig Equations: Algebra

500

solve for x on the interval [0, 360)

sinx + 2 = 3

x = 90

600

solve for x on the interval [0, 360)

2cos²x - sqrt(3)cosx = 0

x = 30, 90, 270, 330

700

solve for x on the interval [0, 2pi)

cos²x + cosx = sin²x

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

800

solve for x on the interval [0, 360)

sinx + cosx = 1

x = 0, 90

1000

solve for all possible values of x

3tan³x - 3tan²x - tanx + 1 = 0

x = 30+360n, 45+360n, 150+360n, 210+360n, 225+360n, 330+360n

Sum Difference, Sum to Product/ Product to Sum

500

Find the exact value of sin(30 + 45)

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

600

Find the exact value of cos(45+60)

sqrt(2) - sqrt(6) / 4

700

Given sin(a) = 3/5, 0 < a < 90, and cos(b) = -5/13, 180 < b < 270

Find sin(a+b)

-63/65

800

Write the product as a sum/difference

2cos(7x / 2)cos(3x / 2)

cos2x + cos4x

1000

Write the following as a product

sin(4x) - sin(2x)

2sinxcos(3x)

Multiple Angles

500

Given that tan(x) = -3/4 and x is in quadrant 2

find sin(2x)

-24/25

600

Given sinx = 5/8, and x is in quadrant 1

find cos(2x)

7/32

700

find the exact value of sin(15) using half angle identities

sqrt(2-sqrt(3)) / 2

800

given tanx = 8 / 15, and x lies in quadrant 3

find cos(x / 2)

-sqrt(17) / 17

1000

simplify the expression so that it is in terms of 1st powers of cosine.

cos⁴x

3/8 + (1/2)cos(2x) + (1/8)cos(4x)