i need help please for calculus

Question

find all the trigonometric values of θ with the given conditions.

 

cos θ = -15/17, sin > 0

Answer 1

Cos Θ = -15/17

 

      Θ = Cos^-1 ( -15 /17 )

 

θ = 151.92^° + 360^°X;   Θ = 180° + 28.08° + 360°X

 

                                     Θ = 208.08° + 360°X

 

Since: SinΘ > 0  this will be true in the II quadrant, but not

                         in the III quadrant

 

Therefor the answer which satisfies all conditions is:

 

    Θ = 151.92 ° + 360°X

 

I read the problem as asking to find the values of Θ that

satisfied the stated conditions.

 

Looking at the problem, the triangle that you would use would be 

in the second quadrant as cos is negative and sin is positive.

As Michael says if you find the third side of the right triangle,

you can then easily get all six trig values.

Answer 2

Use the Pythagorean identity to find sine.  Then the rest will follow.

 

Let   x = θ

 

sinx = √(1 - cos²x)

 

sinx = √(1 - (-15/17)²)

 

 

Simplify this part.  Then to find tangent,

 

tanx = sinx / cosx

 

 

Then the other trig values are as follows:

 

cotx = cosx / sinx

 

sec(x) = 1 / cosx

 

csc(x) = 1 / sinx