identify the identities Technical Mathematics COS A 1 + sin A + 1 + sin A...
6) Use the fundamental identities to find the values of sin(a), tan(a), and sec(a) if cos (a) 3 and tan (a)>0 5 (8 pts)
(7 pts) Use double angle identities to find the indicated value. 13) cos o = sin 0 <0 Find sin(20).
NOTE: Very useful trigonometric identities are these: sin(A B)-sin A cos B sin B cosA, cos(A +B)-COSA cos B-sin A sin B 32. (Bonus problem) A periodic function g(x)is defined on one period like this: g(x).0' on 1<x<0, and it equals x on 0<<1 (a) Give a labeled sketch of the graph of g(x), let's say from-1.5 to 3.5 (b) Give labeled sketches of, the graphs of g (x) and g(x) (i.e, the even and odd parts ofg).
2. Solve the given trigonometric equation using Pythagorian Identities, cos? 0 + sin? 0 = 1, 1+tan? 0 = sec, cot? 0+1 = csc 0. (a) 1 - 2 sin’x = cos r. (b) 4 sin’t - 5 sin x - 2 cos” x = 2. (c) 2 tang - 2 sec1+1= = tan”.
verify the following trigonometric identities. cos y 1-sın y 5, sec y + tany= cos x-sin x -cosx 1-tanx sinx cosx-l 7. sin20+cos 2 θ+ cot 2a 1+tan 2 θ 8.
[6] sin 2B given sec B - 3 cos 2B and & sin >0. In what quadrant does 2B terminate? 7 5 [7] Verify the identity: 2 csc A sin A 1 + cos A + 1 + cos A sin A
prove the identities g. CSC A-sin A = cos A cot A Solution:
cos θ cos φ sin φ sin θ, (Beats) Using the trigonometric identities cos(θ verify that φ) (β a) 2 (19) cos ot - cos Bt 2 sin A spring-mass system has an attached mass of 4 g, a spring constant of 16 g/s* and a negligible friction. It is subject to a force of 4 cos(2.2t) down- ward, and is initially 0 at rest. Determine the subsequent motion. Using (19) from Exercise 11, rewrite the solution as the product...
O TRIGONOMETRIC IDENTITIES AND EQUATIONS Double-angle identities: Problem type 1 3 Find sin 2x, cos 2x, and tan 2x if sinx and x terminates in quadrant III. 10 . 0/0 sin 2x = X5 ? cos 2x tan 2x L
Use sum and difference identities to verify which of the following are identities. 1) sin(Q+8) - 1-tan & tan 8 sin a 2-cot a cot 8 2) cos(a+8) - 2 sin a sin 8 Both the equations are identities. None of the equations are identities Only the first equation is an identity. Only the second equation is an identity.