can someone help me with this question quickly I need it by tomorrow is really confusing pleaseeee......I'm desperate
consider the equation cos^2 θ+ tan^2 θ=2
a.graphically determine a solution to the equation, to the nearest hundredth of a radian.
b.verify the solution by substitution. complete at least one verification for each set of coterminal angle...
pleaseeee help
3 years ago
Answered By Leonardo F
a) As you can see in the graph below, we can plot both sides of the equation. The first solution is: 0.905
b) Checking:
$cos\left(0.905\right)^2+tan\left(0.905\right)^2=0.3815+1.621\approx2$cos(0.905)2+tan(0.905)2=0.3815+1.621≈2
So the solution is correct.
Attached Graph:
3 years ago
Answered By Megan R
a) Make sure your calculator is in radian mode. enter y1 = cos^2(x) + tan^2(x) and y2 = 2
Find an intersection point. The first one in Q1 is at x = 0.90 (rounded to the nearest hundredth)
b) substitute x = 0.9 into cos^2(x) + tan^2(x) = 2
because 0.9 is a rounded value, you will not get a value that is exactly 2, but it will be close to 2.
You must also verify an intersection that is part of a different section of the graph/curve, e.g. x = 2.24 (rounded).
To do this, substitute x = 2.24 into cos^2(x) + tan^2(x) = 2
You will (again) get a value very close to 2.