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can you help me with trigonometric equations?

cos θ=-sin(-θ)
solve each equation on the interval 0≤θ<2Π

2 Answers by Expert Tutors

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Jason S. | My goal is the success of my students. Knowledge-Patience-HonestyMy goal is the success of my students. K...
4.9 4.9 (115 lesson ratings) (115)
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cos^2 = sin^2
 
Since:
cos^2 = 1-sin^2
 
1 - sin^2 = sin^2
 
Add sin^2 to both sides:
 
1 = 2 sin^2
 
Divide by 2:
 
1/2 = sin^2
 
Take the square root:
 
+/- sqrt(2)/2 =  sin (-x)
 
Where is sine +sqrt(2)/2?   pi/4  and 3pi/4
 
Sine is -sqrt(2)/2 at 5pi/4 and 7pi/4.
 
Since,
 
cos(pi/4) = -sin(-pi/4)  
 
cos(5pi/4) = -sin(-5pi/4)
 
 
θ = { pi/4, 5pi/4 }
 

Comments

I like Robert's answer better.
 
Since sin (-x) = -sin (x), you can substitute.
 
cos x = - (-sin x)
cos x = sin x
 
Divide by cos x:
 
cos x = sin x
-----      -----
cos x     cos x
 
1 = tan x
 
My way was the longer and much more difficult way.
Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
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cosθ = -sin(-θ) is equivalent to
tanθ = 1, since sine is an odd function.
Answer: θ = pi/4, 5pi/4