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Name_____________________ Date__________________ Algebra II/Trig Regents Review #10: Trig Part II Converting degrees to radians: multiply by 180 Example: 1. 2. 135 75 Converting radians to degree: multiply by 1. 180 2. 4 or replace pi with 180 5 12 3. 4 radians Example Regents Questions 1. What is the number of degrees in an angle whose radian measure is (1) 150 2. (2) 165 11 ? 12 (3) 330 (4) 518 o What is the radian measure of an angle whose measure is 420 ? (1) 7 3 (2) 7 6 (3) 7 6 (4) 7 3 3. What is the radian measure of the smaller angle formed by the hands of a clock at 7 o’clock? (1) 2 (2) 5 6 (3) 2 3 (4) 4. Find, to the nearest tenth of a degree, the angle whose measure is 2.5 radians. 7 6 Find the Length of the intercepted arc: We use the formula: s r s = intercepted arc = central angle(in radians) r = radius 1. Find the measure of the central angle of a circle with a radius of 2.5 meters and an intercepted arc of 10 meters. 2. If the length of the radius of a circle is 8 meters and the central angle is 30 degrees, finr the length of the intercepted arc. 1. Example Regents Questions A circle has a radius of 4 inches. In inches, what is the length of the arc intercepted by a central angle of 2 radians? (1) 2 2. (3) 8 (2) 2 (4) 8 In circle O, the length of the radius is 8 cm. If the central angle measures 45 o, what is the length of the intercepted arc? Finding the exact value of trig functions with angles in radians: Convert to degrees and use QSRV Example: sin 6 1. Write tan 140 2. Write cot tan 5 3 Example Regents Questions as a function of a positive acute angle. 17 as a function of a positive acute angle (in radians). 18 3. sec 4. tan 4 sin 5. 5 6 5 2 cot 6 23 6 Finding trig values of an unknown angle: **Label each function with the correct sign first** The triangle always starts at the origin** 1. If sin 4 and theta is in Quadrant II. Find the remaining five trig functions. 5 2. If cot 4 and theta is in Quadrant IV, find all other trig functions. 3 Example Regents Questions 1. If sin 2. 3 and tan < 0 , what is the value of cos ? 5 If cos 8 and is in Quadrant I, what is the value of (csc )(tan ) ? 10 Inverse Functions: switching the function value and the angle y arccos x y arcsin x y arctan x 1 y cos x 1 y sin x y tan 1 x Examples: 3 2 arcsin 1. 2. arccos 1 2 3. cos sin 1 2 2 3 5 4. tan sin 1 Example Regents Questions 1. 3 ? 2 What is the principal value of cos1 o (1) 30 o (2) 60 (3) 150 o o (4) 240 2. 3. 5 8 If sin 1 A, then (1) sin A 5 8 (2) sin A 8 5 3 ] 2 Find the value oftan[cos 1 (3) cos A 5 8 (4) cos A 8 5 Cofunctions: sin cos 90 cos sin 90 tan cot 90 cot tan 90 or sec csc 90 csc sec 90 Examples: 1. Find the value of theta for which sin cos15 . 2. Write the expression tan 265 as the function of an acute angle of measure less than 45 . 3. If x is the measure of a positive acute angle, solve for x. sin x 15 cos 2 x Example Regents Questions 1. 2. 2 If A is acute and tan A , then 3 2 (1) cot A 3 (2) cot A 1 3 (3) cot(90 o A) o What is the trigonometric function that isequivalent to sec 35 ? 2 3 (4) cot(90 o A) 1 3