BackSketch an angle θ in standard position such that θ has the least positive measure, and the given point is on the terminal side of θ. Then find the values of the six trigonometric functions for each angle. Rationalize denominators when applicable. See Examples 1, 2, and 4. (―12 , ―5)
Given the right triangle below, use the cosine function to write a trigonometric expression for the missing angle .
Determine the signs of the trigonometric functions of an angle in standard position with the given measure. See Example 2.
178°
Solve each problem. See Examples 1 and 2. Flying Distance The bearing from A to C is N 64° W. The bearing from A to B is S 82° W. The bearing from B to C is N 26° E. A plane flying at 350 mph takes 1.8 hr to go from A to B. Find the distance from B to C.
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. 2x + y = 0 , x ≥ 0
Find the indicated function value. If it is undefined, say so. See Example 4. sec 1800°
Find a value of θ, in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. csc θ = 9.5670466
Solve each problem. See Examples 3 and 4. Height of an Antenna A scanner antenna is on top of the center of a house. The angle of elevation from a point 28.0 m from the center of the house to the top of the antenna is 27°10', and the angle of elevation to the bottom of the antenna is 18°10'. Find the height of the antenna.
In Exercises 1–8, a point on the terminal side of angle θ is given. Find the exact value of each of the six trigonometric functions of θ. (-1, -3)
Identify the quadrant (or possible quadrants) of an angle θ that satisfies the given conditions. See Example 3.
tan θ < 0 , cot θ < 0
In Exercises 1–8, use the Pythagorean Theorem to find the length of the missing side of each right triangle. Then find the value of each of the six trigonometric functions of θ.
Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7.
cos θ = 1
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.) III , r/y