Using the given information, find exact answers to (a), (b) and (c).
Trigonometry: Equations General Outcomes::
File Format: PDF/Adobe Acrobat - View as HTMLThe student should be able to solve trigonometric equations over the. domain of the real numbers. •. Some of the examples or questions could be done with
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cos (A) = 4/5; 0 ° < A < 90°
(a) sin (2A) = 1
(b) cos (2A) = 2
(c) tan (2A) =
Basic Trig::
Looking at the basic trig question , we realize that we have to split the complex trigonometry functions. Before we do that, we multiply the equation by 2
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sin 2A =2sinAcosA =2(3/5)(4/5) =24/25
Solving Trigonometric Equations::
In order to solve trigonometric equations, one must understand how to solve the three basic types of trigonometric equations:. I. cos A = xo. II. sin A = yo
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cos2A =2cos^2A -1 =2(4/5)^2 -1=32/25 -25/25 =7/25
tan2A =sin2A/cos2A = 24/7
Given: cosA = 4/5, then sinA=3/5
a) sin2A = 2sinAcosA = 2*(3/5)*(4/5) =24/25
b) cos2A= cos²A - sin²A = 2cos²A - 1 = 2*(16/25) - 1=(32-25)/25 = 7/25
c) tan2A = sin2A/cos2A = (24/25) / (7/25) [from (a) & (b) above] = 24/7
AJM
AJM
Hi,
If cos A = 4/5, then sin A = 3/5 and tan A = 3/4
sin(2A) = 2 sin A cos A = 2(3/5)(4/5) = 24/25 <==ANSWER
cos(2A) = 1 - 2sin² A = 1 - 2(3/5)² = 7/25 <==ANSWER
tan(2A) = 2 tan A/(1 - tan² A) = 2(3/4)/(1 - (3/4)²) = 24/7 <==ANSWER
I hope that helps!! :-)
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TRIG EQUATION QUESTION?