3. Unit Circle

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

tan s = 0.2126

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

cos s = 0.7826

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

sin s = 0.9918

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

sec s = 1.0806

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

[π/2, π] ; sin s = 1/2

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

[π, 3π/2] ; tan s = √3

Each figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the six circular function values of θ.

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

[3π/2, 2π] ; tan s = -1

Find the exact values of s in the given interval that satisfy the given condition.

[0, 2π) ; sin s = -√3/ 2

Find the exact values of s in the given interval that satisfy the given condition.

[0, 2π) ; sin s = -√3 / 2

Find the exact values of s in the given interval that satisfy the given condition.

[0 , 2π) ; cos² s = 1/2

Find the exact values of s in the given interval that satisfy the given condition.

[-2π , π) ; 3 tan² s = 1

Suppose an arc of length s lies on the unit circle x² + y² = 1, starting at the point (1, 0) and terminating at the point (x, y). (See Figure 12, repeated below.) Use a calculator to find the approximate coordinates for (x, y) to four decimal places.

s = 2.5

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For each value of s, use a calculator to find sin s and cos s, and then use the results to decide in which quadrant an angle of s radians lies.

s = 51

For each value of s, use a calculator to find sin s and cos s, and then use the results to decide in which quadrant an angle of s radians lies.

s = 65