3. Unit Circle

Find each exact function value.

csc ( ―11π/6)

Without using a calculator, determine which of the two values is greater.

tan 1 or tan 2

Without using a calculator, determine which of the two values is greater.

cos 2 or sin 2

Find a calculator approximation to four decimal places for each circular function value.

sin 1.0472

Find a calculator approximation to four decimal places for each circular function value. cos (-0.2443)

Find a calculator approximation to four decimal places for each circular function value.

sec 7.3159

Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.

cos s = 0.9250

Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.

sin s = 0.4924

Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.

cot s = 0.5022

Find the exact value of s in the given interval that has the given circular function value.

[ 0, π/2] ; cos s = √2/2

Find the exact value of s in the given interval that has the given circular function value.

[ π , 3π/2] ; sec s = ―2√3/3

Find the exact values of (a) sin s, (b) cos s, and (c) tan s for each real number s. See Example 1.

s = π/2

A point P(x, y) is shown on the unit circle corresponding to a real number t. Find the values of the trigonometric functions at t.

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A point P(x, y) is shown on the unit circle corresponding to a real number t. Find the values of the trigonometric functions at t.

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The unit circle has been divided into twelve equal arcs, corresponding to t-values of

0, 𝜋/6, 𝜋/3, 𝜋/2, 2𝜋/3, 5𝜋/6, 𝜋, 7𝜋/6, 4𝜋/3, 3𝜋/2, 5𝜋/3, 11𝜋/6, and 2𝜋

Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined.

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sin 𝜋/6