This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1893 edition. Excerpt: ...1. Find sin--and cos in terms of sin A when A lies between 450 arid 630. In this case lies between 225 and 315. From the adjoining figure it is evident that between these limits sin--is greater than cos and is negative. Example 2. Determine the limits between which A must lie in order that 2 cos A =-T ...
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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1893 edition. Excerpt: ...1. Find sin--and cos in terms of sin A when A lies between 450 arid 630. In this case lies between 225 and 315. From the adjoining figure it is evident that between these limits sin--is greater than cos and is negative. Example 2. Determine the limits between which A must lie in order that 2 cos A =-T+sIn24-Jl-sin2A. The given relation is obtained by combining sin4 + cos4 =-N/i + sin24 (1), (2) and From (1), we see that of sin A and cos A the numerically greater is negative. From (2), we see that the cosine is the greater. Hence we have to choose limits between which cos A is numerically greater than sin A and is negative. From the figure we see that A lies between 2nx+ and 2nx +. 4 4 EXAMPLES. XX. a. 1. When A lies between-270 and-360, prove that cos A 119 A A 2. If cos A = tt, find sin--and cos--when A lies be Iby 2 2 tween 270 and 360. 3. If cos A =-, find sin--and cos when A lies between 540 and 630. A A 4. Find sin--and cos-x in terms of sin4 when A lies between 270 and 450. A A A 5. Find sin--and cos--in terms of sin A when--lies between 225 and 315. 4 4. 6. Find sin and cos-in terms of sin A when A lies between-450 and-630. 24 A A 7. If sin 4 =--, find sin-jj and cos--when A lies between 90 and 180. 240 A A 8. If sin A =-, find sin--and cos--when A lies between 270 and 360. 9. Determine the limits between which A must lie in order that A a Thus tan--has the two values tan-and tan z z 262. When any one of the functions of an acute angle A is given, we may in some cases conveniently obtain the functions of--, as in the following example. b A Example. Given cos A =-, to find the functions of g-. Make a right-angled triangle PQR P in which the hypotenuse PQ = a, and. base QIi = b; then cosPQR=Q = b=coSA; / 1 Produce EQ to S making QS =...
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