trigonometry

Question

1.  Find the value of sec 6 pi/7 using a calculator and round to four decimal places.

 

 

2. Given that  Cos theta is -4/square root of 53 and that the terminal side is in quadrant II, find the other five trigonometric function values.

 

3. If Sin theta is square root of 3/2 what is the value of  if  represents an acute angle?

 

Answer 1

1.Sec = 1/cos

Cos 6π/7 = -0.90096887, so sec 6π/7 = -1.10992 = -1.110 (4 places)

 

2. Cos Θ = -4/√53  If you draw a right triangle whose adjacent side  = -4, and whose hypotenuse is √53, then by the Pythagorean Theorem, the opposite side must be  √37 . We are in Quadrant 2.

 

So sinΘ = √37 /√53 = 0.8355, cscΘ √53/√37=  1/0.8355 = 1.1968

     secΘ = -√53/4  = -1.8200

     tanΘ = -√37/4  = -1.5207, cotΘ = -4/√37 = -0.6576

 

3. Do you mean √3/2 ?  If so, Θ = π/3