Math Problem Statement

Match the given function to its graph. ​1) y equals sine left parenthesis x minus StartFraction pi Over 2 EndFraction right parenthesis

​ 2) y equals cosine left parenthesis x plus StartFraction pi Over 2 EndFraction right parenthesis

​3) y equals sine left parenthesis x plus StartFraction pi Over 2 EndFraction right parenthesis ​4) y equals cosine left parenthesis x minus StartFraction pi Over 2 EndFraction right parenthesis A -6 6 -2 2 x y

A coordinate system has a horizontal x-axis labeled from negative 6 to 6 in increments of 2 and a vertical y-axis labeled from negative 2 to 2 in increments of 1. An oscillating periodic curve goes the full length of the graph. In one period, from left to right, the curve starts at minimum at (negative 4.7, negative 1), and rises to cross the x-axis at negative 3.1 and then reaches a maximum at (negative 1.6, 1), and falls to cross the x-axis at 0.0 and reach a minimum at (1.6, negative 1). All coordinates are approximate. B -6 6 -2 2 x y

A coordinate system has a horizontal x-axis labeled from negative 6 to 6 in increments of 2 and a vertical y-axis labeled from negative 2 to 2 in increments of 1. An oscillating periodic curve goes the full length of the graph. In one period, from left to right, the curve starts at minimum at (negative 3.1, negative 1), and rises to cross the x-axis at negative 1.6 and then reaches a maximum at (0.0, 1), and falls to cross the x-axis at 1.6 and reach a minimum at (3.1, negative 1). All coordinates are approximate. C -6 6 -2 2 x y

A coordinate system has a horizontal x-axis labeled from negative 6 to 6 in increments of 2 and a vertical y-axis labeled from negative 2 to 2 in increments of 1. An oscillating periodic curve goes the full length of the graph. In one period, from left to right, the curve starts at a maximum at (negative 3.1, 1), and falls to cross the x-axis at negative 1.6 and then reaches a minimum at (0.0, negative 1), and rises to cross the x-axis at 1.6 and reach a maximum at (3.1, 1). All coordinates are approximate. D -6 6 -2 2 x y

A coordinate system has a horizontal x-axis labeled from negative 6 to 6 in increments of 2 and a vertical y-axis labeled from negative 2 to 2 in increments of 1. An oscillating periodic curve goes the full length of the graph. In one period, from left to right, the curve starts at a maximum at (negative 4.7, 1), and falls to cross the x-axis at negative 3.1 and then reaches a minimum at (negative 1.6, negative 1), and rises to cross the x-axis at 0.0 and reach a maximum at (1.6, 1). All coordinates are approximate. Question content area bottom Part 1 A. ​1B, 2D,​ 3C, 4A B. ​1A, 2D,​ 3C, 4B C. ​1A, 2B,​ 3C, 4D D. ​1C, 2A,​ 3B, 4D

Solution

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Sine and Cosine Functions
Phase Shifts
Graph Transformations

Formulas

y = sin(x ± a)
y = cos(x ± a)

Theorems

Phase Shift in Trigonometric Functions
Graphing Transformations of Trigonometric Functions

Suitable Grade Level

Grades 9-12