2. Trigonometric Functions on Right Triangles

What is the positive value of P in the interval $\(\left\)[0\(\degree\),90\(\degree\]\right\))$ that will make the following statement true? Express the answer in four decimal places.

$\(\cot\) P=5.2371$

Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7.

sin θ = √5/7 , and θ is in quadrant I.

Identify the quadrant (or possible quadrants) of an angle θ that satisfies the given conditions. See Example 3.

csc θ > 0 , cot θ > 0

In Exercises 23–34, find the exact value of each of the remaining trigonometric functions of θ. tan θ = -2/3, sin θ > 0

Identify the quadrant (or possible quadrants) of an angle θ that satisfies the given conditions. See Example 3.

tan θ < 0 , cos θ < 0

Determine whether each statement is possible or impossible. c. cos θ = 5

In Exercises 23–34, find the exact value of each of the remaining trigonometric functions of θ. cos θ = 8/17, 270° < θ < 360°

Use trigonometric function values of quadrantal angles to evaluate each expression. tan 360° + 4 sin 180° + 5(cos 180°)²

CONCEPT PREVIEW Determine whether each statement is possible or impossible. cos θ = 1.5

Determine whether each statement is possible or impossible. b. tan θ = 1.4

Solve each problem. (Source for Exercises 49 and 50: Parker, M., Editor, She Does Math, Mathematical Association of America.) Create a right triangle problem whose solution can be found by evaluating θ if sin θ = ¾.

Find the indicated function value. If it is undefined, say so. See Example 4. sin(―270°)

Use trigonometric function values of quadrantal angles to evaluate each expression. [cos(―180°)]² + [sin(― 180°)]²