Simplify without using the calculator or the sin tables.

1/8

Step-by-step explanation:

sin²(π/8) − cos⁴(3π/8)

Use power reduction formulas:

1/2 (1 − cos(2×π/8)) − 1/8 (3 + 4 cos(2×3π/8) + cos(4×3π/8))

Simplify:

1/2 (1 − cos(π/4)) − 1/8 (3 + 4 cos(3π/4) + cos(3π/2))

1/2 (1 − √2/2) − 1/8 (3 + 4 (-√2/2) + 0)

1/2 − √2/4 − 1/8 (3 − 2√2)

1/2 − √2/4 − 3/8 +√2/4

1/2 − 3/8

1/8

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.