...form a right-angled triangle CDE or CDH, of which the radius CD is the hypothenuse ; and therefore the square of the radius is equal to the sum of the squares of the sine and cosine of any arc, that is, CD* = CE* -*- ED* or = сн1 -i- DH*. It is evident...

...sura of the squares of the chord of an arc, and of the chord of its supplement to a semi-circle. 2. The square of the radius is equal to the sum of the squares of the sine and co-sine. 3. The sum of the co-sine and versed-sine is equal to the radius....

...tan(90° — a) ; &c. (303) seca = cosec(90° — a), coseca = sec(90° — a) ; &c. (304) PROPOSITION I. The sum of the squares of the sine and cosine of an arc (305) is equal to the square of the radius, or to unity, when the radius is taken for the unit...

...the sine of half that arc : Thus BG = ^BL. 2. In the right-angled triangle CGB, CB2 = CG2 + GB2, or the square of the radius is equal to the sum of the squares of the sine and cosine of any arc; hence sin. = /J(R3 — cos.2), cos. = V(R2 — sin.2), or...

...cos A' cos A' The theorem is, therefore, true for all angles that do not exceed two right angles. 39. The sum of the squares of the sine and cosine of an angle is equal to I. The right-angled triangle ACB (28) gives BCs-|-AC2 = AB2 ; substituting for the...

...the sum of the squares of the chord of an arc, and of the chord of its supplement to a semicircle. 2. The square of the radius is equal to the sum of the squares of the sine and cosine. 3. The sum of the cosine and versed- sine is equal to the radius. 4....

...T~+ cos / 21T/1 27T/2 , 2T/1 . 2lT/J\ + 2r1r. ^cos-j, • cos „, + sin „- • sin „, J • But the sum of the squares of the sine and cosine of an angle is equal to unity,1 and the sum of the product of the sines and cosines of two angles is equal...

...cosine of its supplement, respectively, § 457, the same relation holds for obtuse angles. Hence : The sum of the squares of the sine and cosine of an (oblique) angle is equal to unity. 459. EXERCISES 1. Given A an acute angle and sin A = f ; find cos...

...TRIGONOMETRIC FUNCTIONS AND THEIR APPLICATIONS I sin2 x + cos2 x = I ... (I) This expression states that the sum of the squares of the sine and cosine of an angle is identically equal to unity. 1dentically equal means that it is true for any value of л ,...

...less than 360° (2n rad). CHAPTER 11 Trigonometric Functions PYTHAGOREAN THEOREM FOR SINE AND COSINE The sum of the squares of the sine and cosine of an angle is always equal to 1 . The following formula holds: sin2 9 + cos2 9= 1 A NOTE ABOUT EXPONENTS...