if 0< theta < 90 and tan theta equals pie3/2, find cos theta.i put 2/pie 7 but i was wrong please correct.
I don't know what you mean by
pie3/2 and by 2/pie 7
do you mean 3pi/2 ? or ???
2/pie 7 is even more confusing.
remember tan(theta) = opposite/ adjacent
so you can form a right-angled triangle in the first quadrant, fill in those two sides, then use Pythagoras to find the hypotenuse.
And cos(theta) = adjacent/hypotenuse
my nswers was 2/pi7 but i ws wrong
you did not answer my question.
What do you mean by 2/pi7 ???
do you mean 2/(7pi) ? or (2/pi)(7) ? or ...
write it as (numerator)/(denominator)
sorry my nswer was 2/(7 pi) but it ws wrong
To find the value of cos(theta), we can use the given information that tan(theta) = pi/3/2. Since tan(theta) = sin(theta)/cos(theta), we can rewrite the equation as sin(theta)/cos(theta) = pi/3/2.
To solve for cos(theta), we need to isolate it. Multiply both sides of the equation by cos(theta):
sin(theta) = (pi/3/2) * cos(theta)
Now, let's rewrite pi/3/2 as pi/3 * 2:
sin(theta) = (pi/3) * 2 * cos(theta)
Divide both sides of the equation by (pi/3) * 2:
sin(theta) / ((pi/3) * 2) = cos(theta)
Simplify the expression on the left side:
sin(theta) * (3/(2pi)) = cos(theta)
Now we have an equation with sin(theta) and cos(theta) on the same side. We can use the Pythagorean identity sin^2(theta) + cos^2(theta) = 1 to solve for cos(theta).
Using this identity, we can substitute sin^2(theta) with 1 - cos^2(theta):
(1 - cos^2(theta)) * (3/(2pi)) = cos(theta)
Distribute the (3/(2pi)):
(3/(2pi)) - (3/(2pi)) * cos^2(theta) = cos(theta)
Move the cos(theta) term to the left side:
(3/(2pi)) * cos^2(theta) + cos(theta) - (3/(2pi)) = 0
This is now a quadratic equation. Let's solve for cos(theta) by factoring or using the quadratic formula:
(3/(2pi)) * cos^2(theta) + cos(theta) - (3/(2pi)) = 0
Multiply the equation by 2pi to eliminate the fraction:
3 * cos^2(theta) + 2pi * cos(theta) - 3 = 0
Now, you can solve this quadratic equation by factoring or by using the quadratic formula:
cos(theta) = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 3, b = 2pi, and c = -3. Plug these values into the quadratic formula:
cos(theta) = (-(2pi) ± √((2pi)^2 - 4(3)(-3))) / (2(3))
cos(theta) = (-2pi ± √(4pi^2 + 36)) / 6
After simplifying, you will get the value(s) of cos(theta). Make sure to choose the appropriate value based on the given condition 0 < theta < 90.