Find the exact values of the six trig functions for pi/6 radians?

Question

sin pi/6

cos pi/6

tan pi/6

csc pi/6

sec pi/6

cot pi/6

simplify but do not aproximate radicals

Answer 1

• sin (π/6).

π/6 is in quadrant 1 and there is no need for either coterminal or reference angles.

In quadrant 1 the sin is positive.

So, sin (π/6) is evalueated directly as follows.

⇒ sin (π/6) = 1/2.

• cos (π/6).

π/6 is in quadrant 1 and there is no need for either coterminal or reference angles.

In quadrant 1 the sin is positive.

So, cos (π/6) is evalueated directly as follows.

⇒ cos (π/6) = √3/2.

• tan (π/6).

π/6 is in quadrant 1 and there is no need for either coterminal or reference angles.

In quadrant 1 the sin is positive.

So, tan (π/6) is evalueated directly as follows.

tan (π/6) = sin (π/6)/cos (π/6) = (1/2)/(√3/2) = 1/√3.

⇒ tan (π/6) = 1/√3.

• csc (π/6).

Using the reciprocal identity csc (π/6) = 1/sin (π/6).

csc (π/6) = 1/(1/2) = 2.

⇒ csc (π/6) = 2.

• sec (π/6).

Using the reciprocal identity sec (π/6) = 1/cos (π/6).

sec (π/6) = 1/(√3/2) = 2/√3.

⇒ sec (π/6) = 2/√3.

• cot (π/6).

Using the reciprocal identity cot (π/6) = 1/tan (π/6).

cot (π/6) = 1/(1/√3) = √3.

⇒ cot (π/6) = √3.