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# ​ What is the value of cos(−θ) ?

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What is the value of cos(−θ)?

SamJones  Mar 4, 2018

#1
+6608
+3

By the Pythagorean identity...

sin2(-θ) + cos2(-θ)   =   1

Plug in  (-3/5)  for  sin(-θ)

(-3/5)2 + cos2(-θ)   =   1

9/25   +  cos2(-θ)   =   1

Subtract  9/25  from both sides of the equation.

cos2(-θ)   =   1  -  9/25

cos2(-θ)   =   16/25

Take the  ±  square root of both sides.

cos(-θ)   =   ±√[ 16/25 ]

cos(-θ)   =   ± 4 / 5

Since  sin(-θ)  is negative,  -θ  must lie in Quadrant III or Quadrant IV.

Since  tan θ  is positive,  θ  must lie in Quadrant I or III, and so  -θ  must lie in Quadrant II or IV.

So  -θ  must lie in Quadrant IV, and  cos(-θ)  must be positive.

cos(-θ)   =   4 / 5

hectictar  Mar 4, 2018
Sort:

#1
+6608
+3

By the Pythagorean identity...

sin2(-θ) + cos2(-θ)   =   1

Plug in  (-3/5)  for  sin(-θ)

(-3/5)2 + cos2(-θ)   =   1

9/25   +  cos2(-θ)   =   1

Subtract  9/25  from both sides of the equation.

cos2(-θ)   =   1  -  9/25

cos2(-θ)   =   16/25

Take the  ±  square root of both sides.

cos(-θ)   =   ±√[ 16/25 ]

cos(-θ)   =   ± 4 / 5

Since  sin(-θ)  is negative,  -θ  must lie in Quadrant III or Quadrant IV.

Since  tan θ  is positive,  θ  must lie in Quadrant I or III, and so  -θ  must lie in Quadrant II or IV.

So  -θ  must lie in Quadrant IV, and  cos(-θ)  must be positive.

cos(-θ)   =   4 / 5

hectictar  Mar 4, 2018

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