2. Trigonometric Functions on Right Triangles

If n is an integer, n • 180° represents an integer multiple of 180°, (2n + 1) • 90° represents an odd integer multiple of 90° , and so on. Determine whether each expression is equal to 0, 1, or ―1, or is undefined. sin[270° + n • 360°]

In Exercises 69–70, express the exact value of each function as a single fraction. Do not use a calculator. If f(θ) = 2 cos θ - cos 2θ, find f(𝜋/6).

Find the bearing from O to A.

Determine whether each statement is true or false. If false, tell why. Use a calculator for Exercises 39 and 42. 1 tan² 60° = sec² 60°

Concept Check Suppose that the point (x, y) is in the indicated quadrant. Determine whether the given ratio is positive or negative. Recall that r = √(x² + y²) .(Hint: Drawing a sketch may help.) II , y/x

In Exercises 33–42, let sin t = a, cos t = b, and tan t = c. Write each expression in terms of a, b, and c.

cos t + cos(t + 1000𝜋) - tan t - tan(t + 999𝜋) - sin t + 4 sin(t - 1000𝜋)

Solve each problem. See Examples 3 and 4. The figure to the right indicates that the equation of a line passing through the point (a, 0) and making an angle θ with the x-axis is y = (tan θ) (x - a). Find an equation of the line passing through the point (5, 0) that makes an angle of 15° with the x-axis.

Determine whether each statement is possible or impossible. a. sec θ = ―2/3

Concept Check Suppose that 90° < θ < 180° .   Find the sign of each function value. cot (θ + 180°)

Use trigonometric function values of quadrantal angles to evaluate each expression. ―3(sin 90°)⁴ + 4(cos 180°)³

Find the indicated function value. If it is undefined, say so. See Example 4. tan 450°

Use trigonometric function values of quadrantal angles to evaluate each expression. (sec 180°)² ― 3 (sin 360°)² + cos 180°

An equation of the terminal side of an angle θ in standard position is given with a restriction on x. Sketch the least positive such angle θ , and find the values of the six trigonometric functions of θ . See Example 3. ―5x ― 3y = 0 , x ≤ 0

What is the positive value of $D$ in the interval $\(\left\)[0,\(\frac{\pi}{2}\]\right\))$ that will make the following statement true? Express the answer in four decimal places.

$\(\sec\) D=3.2842$