Trigonometry

Question

Use trig properties to find the exact value of (sin70/cos-430)+(tan-70).  Show your work.

Answer 1

cosθ = cos(θ+360°)

 

So, cos(-430°) = cos(-430°+360°) = cos(-70°)

 

Since y = cosθ is an even function (graph is symmetric with respect to the y-axis), cos(-θ) = cosθ.  So, cos(-70°) = cos(70°).

 

Since y = tanθ is an odd function (symmetric with respect to the origin), tan(-θ) = -tanθ.  So, tan(-70°) = -tan70°.

 

Therefore, sin(70°)/cos(-430°) + tan(-70°)

 

               = sin(70°)/cos(70°) - tan(70°) = tan(70°) - tan(70°) = 0