Question

explain how to graph y=sinx+cosx

Answer 1

First, transform y into a product having only one trig function. Use the trig identity sin a + sin b = 2sin (a + b)/2*cos (a - b)/2
y = sin x + cos x = sin x + sin (Pi/2 - x) = V2*sin (x + pi/4).
Now, graph the function y. The period is 2Pi
x = 0 -> sin (x + Pi/4) = sin Pi/4 = V2/2 -> y = V2*V2/2 = 1
x = Pi/4 -> sin (x + Pi/4) = 1 -> y = V2
x = Pi/2 -> sin (x + Pi/4) = sin 3Pi/4 -> y = V2*V2/2 = 1
x = 3Pi/4 -> sin (x + Pi/4) = sin Pi = 0 -> y = 0
Continue, then create a Variation Table , with x varies from 0 to 2Pi. Find the related values of y, then graph the function.

x | 0 Pi/4 Pi/2 3Pi/4 Pi 5Pi/4 3Pi/2 7Pi/4 2Pi
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y | 1 V2 1 0