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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

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

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 }

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.