# Math

posted by .

What is the exact answer to cos^2x - sin^2x = 0 for between 0 and 2pi?

I got x = pi/4 and x = 5pi/4. But the answer key says there are two additional answers which are 3pi/4 and 7pi/4. I don't know how to get these. Any help is much appreciated!

• Math -

cos^2x - sin^2x = 0
cos (2x) = 0
2x = π/2 or 2x = 3π/2

x = π/4 or π = 3π/4

but the period of cos (2x) is π
π/4+π = 5π/4
3π/4 + π = 7π/4

Since I converted to cos 2x, there would be 2 complete cosine curves for 0 to 2π

other way:

cos^2 x = sin^2 x
sin^2 x/cos^2 x = 1
tan ^2 x = 1
tan x = ± 1
x = 45°, 135° , 225° , 315°
or
π/4 , 3π/4 , 5π/4 , 7π/4

• Math -

Thanks!

• Math -

There is an expression some people use that says, “What you put into it is what you get out of it.” People might use this expression to describe your skills at a sport or activity and how that relates to the amount of time and effort you spend practicing that activity. Does this expression apply to functions? How?

• Math -

There is an expression some people use that says, “What you put into it is what you get out of it.” People might use this expression to describe your skills at a sport or activity and how that relates to the amount of time and effort you spend practicing that activity. Does this expression apply to functions? How? Give an example to support your answer.

djakjsnjkajndjkjckjsdnkjnckjansdkjnckjandskjnkajdnkjnkajndkjsndkjsndkjsnkjdnkjandsk

## Similar Questions

State the period and phase shift of the function y=-4tan(1/2x + 3pi/8) a) 2pi, -3pi/4 b) pi, 3pi/8 c) 2pi, 3pi/8 d) pi, -3pi/8 Answer: d 2) What is the equation for the inverse of y=cos x+3: a) y=Arccos(x+3) b) y=Arccos x-3 c) y=Arccos …
2. ### math

Evaluate. 1. sin^-1(-1/2) 2. cos^-1[(-root 3)/2] 3. arctan[(root3)/3] 4. cos(arccos2/3) 5. arcsin(sin 2pi) 6. sin(arccos 1) I got these values as my answers: 1. -pi/6 2. 5pi/6 3. pi/6 4. 2/3 5. 2pi 6. 0 Can someone please tell me if …

Approximate the equation's solutions in the interval (0,2pi) sin2x sinx = cosx 2cos(x) (1/2-sin^2x) = 0 Then I got 3pi/2, pi/2, pi/6 and 5pi/6 Then I substituted 0-3 and got 3pi/2 , 5pi/2 , 9pi/2 , pi/2, pi/6, 7pi/6, 13pi/6 , 19pi/6 …
4. ### trig

Solve the equation for cos theta-tan theta=0 for greater than or egual to zero but less than 2pi. Write your answer as a multiple of pi, if possible form the following choices: pi , 5pi A. --- ---- 4___ 4 B. pi 3pi 5pi 7pi ----- '----- …
5. ### math

Use the exact values of the sin, cos and tan of pi/3 and pi/6, and the symmetry of the graphs of sin, cos and tan, to find the exact values of si -pi/6, cos 5/3pi and tan 4pi/3. I have found the answers to the first three using the …
6. ### math

Use the exact values of the sin, cos and tan of pi/3 and pi/6, and the symmetry of the graphs of sin, cos and tan, to find the exact values of sin -pi/6, cos 5/3pi and tan 4pi/3. I have found the answers to the first three using the …
7. ### trig

Solve cos x-1 = sin^2 x Find all solutions on the interval [0,2pi) a. x=pi, x=pi/2, x= 2pi/3 b. x=3pi/7, x=pi/2, x=2pi/3 c. x=3pi/7, x=3pi/2, x=3pi/2 d. x=pi, x=pi/2, x=3pi/2
8. ### Math

1. On the interval [0, 2pi] what are the solutions to the equation sin3xcos2x = -cos3xsin2x + 1?