cos θ = 1 2 and θ terminates in QIV

Question

Find the remaining trigonometric functions of θ based on the given information.
cos θ = 
1
2
and θ terminates in QIV

Answer 1

I assume this is saying cos Θ = 1/2

 

Then we know that sec Θ = 1/cos Θ = 1/(1/2) = 2

 

Thinking of the 30-60-90° triangles, we know that cos (π/3) = 1/2 and sin (π/3) = √3/2

 

In Quadrant IV, sine is negative, so sin Θ = -√3/2

 

csc Θ = 1/sin Θ = -2/√3 = (-2√3)/3

 

The tangent and cotangent functions are also negative in Quadrant IV

 

tan (π/3) = √3, so tan Θ = -√3

 

cot Θ = 1/tan Θ = -1/√3 = -√3/3

Answer 2

Do you mean 

 

cosθ = 1/2 ?

 

(If so, why not just write it that way?)

 

I assume that is what you meant.

 

θ = cos^-1(0.5) = 60°

 

Quadrant IV ⇒ θ = (360 - 60)° = 300° = (2π - π/3) rad = 5π/3 rad

 

θ = 300° = 5π/3 rad

 

Now just evaluate the trigonometric functions.