no 80: show that the function f(x) = 1 (rational) =0 (irrational) is periodic but has no period.

-1, then /1 and /2 intersect at right angles. Show that if , and /2 do not intersect at right angles, then the angle a between dius r, a sector with a central 1 and /2 (see Section 1.4) is given by the formula . Take 0 between 0 and 21. m1 - m2 metric fine tan a = 1 + mim2 gure 1.6. 11. (s) x in the interval [0, 2x ] HINT: Derive the identity onleos COS x = -1/2. tan 01 - tan 02 tan(01 - 02) = sin x = 1. 1 + tan 01 tan 02 in 2x = - V3/2. by expressing the right side in terms of sines and cosines. an x = -V3. Exercises 76-79. Find the point where the lines intersect and determine the angle between the lines. imal place accuracy. S 170. 76. 11: 4x - y - 3=0, 12:3x - 4y+1=0. 77. 1 : 3x + y - 5=0, 12:7x -10y +27 =0. s(-13.461). t(7.31 1). 78. 11 : 4x - y + 2 =0, 12: 19x + y=0. 79. 11 : 5x - 6y + 1 =0, 12: 8x + 5y+2=0. ne opposite that are in the interval 1, x rational s and use four decimal 80. Show that the function f(x) = 1 0. x irrational is periodic but has no period. x =-0.8243. 81. Verify that, for angles 0 between 0 and it /2, the definition r = -3.0649. of the trigonometric functions in terms of the unit circle and c = 10.260. the definitions in terms of a right triangle are in agreement. HINT: Set the triangle as in the figure. = yo for x in [0, 2x ] graph of f and the line YA function to find the (cos 0, sin 0) range c "he func- ty plane, To (1, 0) x vention, we' sin x + co x. 1 + sin x. Vcos2 x. least positive m- The setting for Exercises 82, 83, 84 is a triangle with sides a, b, c and opposite angles A, B, C. cos 2x. 82. Show that the area of the triangle is given by the formula A = =ab sin C. in -x. 83. Confirm the law of sines