Trigonometric Functions on the Unit Circle: Videos & Practice Problems

Determine the trigonometric function values at P(x,y) for the real number represented by the point P on the unit circle.

The circle with a radius of one unit is partitioned into twelve equal arcs, where each arc corresponds to specific t-values. Determine the value of the trigonometric function at the given real number t using the (x,y) coordinates in the diagram or specify that the expression is undefined.

sin(2π/3)

The circle with a radius of one unit is partitioned into twelve equal arcs, where each arc corresponds to specific t-values. Determine the value of the trigonometric function at the given real number t using the (x,y) coordinates in the diagram or specify that the expression is undefined.

cos(5π/3)

The circle with a radius of one unit is partitioned into twelve equal arcs, where each arc corresponds to specific t-values. Determine the value of the trigonometric function at the given real number t using the (x,y) coordinates in the diagram or specify that the expression is undefined.

cot 0

The circle with a radius of one unit is partitioned into twelve equal arcs, where each arc corresponds to specific t-values. Determine the value of the trigonometric function at the given real number t using the (x,y) coordinates in the diagram or specify that the expression is undefined.

csc(7π/6)

The circle with a radius of one unit is partitioned into twelve equal arcs, where each arc corresponds to specific t-values. Determine the value of the trigonometric function at the given real number t using the (x,y) coordinates in the diagram or specify that the expression is undefined.

sec(7π/6)

The circle with a radius of one unit is partitioned into twelve equal arcs, where each arc corresponds to specific t-values. Determine the value of the trigonometric function at the given real number t using the (x,y) coordinates in the diagram or specify that the expression is undefined.

cos 0

The circle with a radius of one unit is partitioned into twelve equal arcs, where each arc corresponds to specific t-values. Determine the value of the trigonometric function at the given real number t using the (x,y) coordinates in the diagram or specify that the expression is undefined.

csc π

The circle with a radius of one unit is partitioned into twelve equal arcs, where each arc corresponds to specific t-values. Determine the value of the trigonometric function at the given real number t using the (x,y) coordinates in the diagram or specify that the expression is undefined. Also, find out the value in part b) using even and odd properties of trigonometric functions.

a. cos(4π/3)

b. cos(-4π/3)

The circle with a radius of one unit is partitioned into twelve equal arcs, where each arc corresponds to specific t-values. Determine the value of the trigonometric function at the given real number t using the (x,y) coordinates in the diagram or specify that the expression is undefined. Also, find out the value in part b) using even and odd properties of trigonometric functions.

a. cos(7π/6)

b. cos(-7π/6)

The circle with a radius of one unit is partitioned into twelve equal arcs, where each arc corresponds to specific t-values. Determine the value of the trigonometric function at the given real number t using the (x,y) coordinates in the diagram or specify that the expression is undefined. Also, find out the value in part b) using even and odd properties of trigonometric functions.

a. sin(7π/6)

b. sin(-7π/6)

The circle with a radius of one unit is partitioned into twelve equal arcs, where each arc corresponds to specific t-values. Determine the value of the trigonometric function at the given real number t using the (x,y) coordinates in the diagram or specify that the expression is undefined. Also, find out the value in part b) using even and odd properties of trigonometric functions.

a. tan(7π/6)

b. tan(-7π/6)

The circle with a radius of one unit is partitioned into twelve equal arcs, where each arc corresponds to specific t-values. Determine the value of the trigonometric function at the given real number t using the (x,y) coordinates in the diagram or specify that the expression is undefined. Also, find out the value in part b) using even and odd properties of trigonometric functions.

a. cot(11π/6)

b. cot(-11π/6)

The circle with a radius of one unit is partitioned into eight equal arcs, where each arc corresponds to specific values. Determine the value of the trigonometric function at the given real number using the (x,y) coordinates in the diagram or specify that the expression is undefined. Also, find out the value in part b) using periodic properties of trigonometric functions.

a. sin(5π/4)

b. sin(13π/4)

The circle with a radius of one unit is partitioned into eight equal arcs, where each arc corresponds to specific values. Determine the value of the trigonometric function at the given real number using the (x,y) coordinates in the diagram or specify that the expression is undefined. Also, find out the value in part b) using periodic properties of trigonometric functions.

a. cos(3π/2)

b. cos(11π/2)

The circle with a radius of one unit is partitioned into eight equal arcs, where each arc corresponds to specific values. Determine the value of the trigonometric function at the given real number using the (x,y) coordinates in the diagram or specify that the expression is undefined. Also, find out the value in part b) using periodic properties of trigonometric functions.

a. sec(π)

b. sec(13π)

The circle with a radius of one unit is partitioned into eight equal arcs, where each arc corresponds to specific values. Determine the value of the trigonometric function at the given real number using the (x,y) coordinates in the diagram or specify that the expression is undefined. Also, find out the value in part b) using periodic properties of trigonometric functions. 

a. cot(3π/2) 

b. cot(19π/2)

The circle with a radius of one unit is partitioned into eight equal arcs, where each arc corresponds to specific values. Determine the value of the trigonometric function at the given real number using the (x,y) coordinates in the diagram or specify that the expression is undefined. Also, find out the value in part b) using periodic properties of trigonometric functions. 

a. sin(3π/4) 

b. sin(43π/4)

Determine the six circular function values of θ. The angle θ is in standard position and the terminal side intersects the unit circle at the specified point.

Determine the six circular function values of θ. The angle θ is in standard position and the terminal side intersects the unit circle at the specified point.

Determine the exact values of sin p, cos p, and tan p where p = 6π.

Determine the exact values of sin p, cos p, and tan p where p = -7π.

Determine the exact value of the given function.

cos (-7π/3)

Determine the exact value of the given function.

cos (5π/4)

Determine the exact value of the given function.

sin (-5π/3)

Determine the exact value of the given function.

sec (47π/6)

Determine the exact value of the given function.

tan (11π/6)

Determine the value of the given trigonometric circular function with the help of a calculator. Round the answer to four decimal places.

sin 0.4528

Determine the value of the given trigonometric circular function with the help of a calculator. Round the answer to four decimal places.

cos (-2.2685)

Determine the value of the given trigonometric circular function with the help of a calculator. Round the answer to four decimal places.

tan 7.2198