Solving Trigonometric Equations


For Exercises 51–54, solve for the angle θ, where 0 ≤ θ ≤ 2π.


sin² θ = cos² θ

Even and Odd Functions

In Exercises 47–62, say whether the function is even, odd, or neither. Give reasons for your answer.

sin x²

Increasing and Decreasing Functions

Graph the functions in Exercises 37–46. What symmetries, if any, do the graphs have? Specify the intervals over which the function is increasing and the intervals where it is decreasing.

y = −x³

Graph the functions in Exercises 37–56.

y = (x + 1)²/³

Finding Formulas for Functions

Express the side length of a square as a function of the length d of the square’s diagonal. Then express the area as a function of the diagonal length.

Shifting Graphs

Exercises 27–36 tell how many units and in what directions the graphs of the given equations are to be shifted. Give an equation for the shifted graph. Then sketch the original and shifted graphs together, labeling each graph with its equation.

y = x³ Left 1, down 1

General Sine Curves

For

f(x) = A sin ((2π/B)(x – C) +D

identify A, B, C, and D for the sine functions in Exercises 67–70 and sketch their graphs.

y = ½ sin (πx – x) + ½