Question

Find the values of the six trigonometric functions of theta with the given constraint.

Answer 1

Answer:

Step-by-step explanation:

tan θ is undefined at θ=π/2 and 3π/2

sin π/2=1

cos π/2=0

tanπ/2=undefined

csc π/2=1

sec π/2= undefined

cot π/2=0

sin 3π/2=sin (π+π/2)=-sin π/2=-1

cos 3π/2=cos (2π-π/2)=cosπ/2=0

tan (3π/2)=tan (π+π/2)=tanπ/2=undefined

csc 3π/2=csc (π+π/2)=-csc π/2=-1

sec 3π/2=sec(2π-π/2)=secπ/2=undefined

cot 3π/2=cot(π+π/2)=cotπ/2=0

Answer 2

Answer:

The six trig ratios at 3pi/2 are:

sin(3pi/2)=-1

cos(3pi/2)=0

tan(3pi/2) (undefined)

csc(3pi/2)=-1

sec(3pi/2) (undefined)

cot(3pi/2)=0

Step-by-step explanation:

If tangent is undefined then cosine would have to be 0 given that tangent is the ratio of sine to cosine.

cosine is 0 at pi/2 and 3pi/2 in the first rotation of the unit circle.

3pi/2 satisfies the given constraint.

The six trig ratios are therefore:

sin(3pi/2)=-1

cos(3pi/2)=0

tan(3pi/2)=-1/0 (undefined)

Reciprocal values:

csc(3pi/2)=-1

sec(3pi/2) undefined since cos(3pi/2)=0

cot(3pi/2)=0/-1=0