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Sketch graphs of sinxandcosxon-2π,2π.

(a) Use the graph of sinxto determine where sinxis increasing and where it is decreasing.

(b) Use the graph of cosxto determine where cosxis positive and where it is negative.

(c) Explain why your answers to parts (a) and (b) suggest that cosxis the derivative of sinx.

Short Answer

Expert verified

(a) The graph of sinxincreases at -π2to-3π2,0toπ2,3π2to2πand decreases at localid="1648770535664" π2to3π2,0to-π2,-3π2to-2π.

(b) The graph of cosxis positive at -π2toπ2,3π2to2π,-3π2to-2πand negative at π2to3π2,-3π2to-π2.

(c) Intervals where the graph of sinxincreases and decreases are opposite of cosx,so cosxmight be derivative ofsinx.

Step by step solution

01

Step 1. Given information.  

The given trigonometric Functions aresinxandcosxon-2π,2π.

02

Step 2. Graph of trigonometric functions.

Plot the graph of sinxon-2π,2π.

The graph of sinxstates that the function increases at -π2to-3π2,0toπ2,3π2to2π.

The graph of sinxstates that the function decreases atπ2to3π2,0to-π2,-3π2to-2π.

03

Step 3. Part (b)

Plot the graph of cosxon-2π,2π.

The graph of cosxstates that the function is positive at-π2toπ2,3π2to2π,-3π2to-2π.

The graph of cosxstates that the function is negative atπ2to3π2,-3π2to-π2.

04

Step 4. Part (c)

plot the graph ofsinxandcosxon-2π,2π.

Intervals where the graph of sinxincreases and decreases are opposite ofcosx.

so cosxmight be derivative of sinx.

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