solve each equation find all solutions in the interval 0 2π)
leave your answers in the exact form.
a) sin θ = cos(2θ)
b) sin (2θ) + cos(2θ) = √2/2
c) cos^3 + cos^2 - 3 cosθ - 3 = 0
d) sin 5x - sin 3x = cos 4x
e)sin(3x) + sin^2(x) + cos^2(x) = tan^2(x) - sec^2(x)
cosxdx + [7+(2/y)]sinxdy = 0
Find if the equation is exact. If it is exact, solve.
If it is not exact, find an integrating factor to make it exact,
verify that it is exact and solve it.
Solve the given equation. (Enter your answers as a
comma-separated list. Let k be any integer. Round terms to
three decimal places where appropriate. If there is no solution,
enter NO SOLUTION.)
cos2(θ) − cos(θ) − 12 = 0
Solve the given equation. (Enter your answers as a
comma-separated list. Let k be any integer. Round terms to
three decimal places where appropriate. If there is no solution,
enter NO SOLUTION.)
cos(θ) − sin(θ) = 1
a) Determine whether the given differential equation is exact.
If it is exact, solve it. (If it is not exact, enter NOT.)
(2xy2 − 5) dx + (2x2y + 4) dy = 0
b) Solve the given differential equation by finding, as in
Example 4 of Section 2.4, an appropriate integrating factor.
(6 − 20y +
e−5x)
dx − 4 dy = 0
Use your graphing calculator to find the solutions to the
following equation for
0° ≤ θ < 360°
by defining the left side and right side of the equation as
functions and then finding the intersection points of their graphs.
Make sure your calculator is set to degree mode. (Round your
answers to one decimal place. Enter your answers as a
comma-separated list. If there is no solution, enter NO
SOLUTION.)
3 sin2 θ + 1 = 5 sin θ
Determine whether the given differential equation is exact. If
it is exact, solve it.
i) (x 3 + y 3 )dx + 3xy2 dy = 0, Ans. x 4 + 4y 3x = C
ii) (y ln y − e −xy) + (1 y + x ln y) dy dx = 0, Ans. not
exact
iii) (e −x sin y − 3)dx − (3x 2 − e x sin(2y))dy = 0, Ans. not
exact
iv) (xy − 1)dx + (x...
Solve ΔABC. (Round your answers to two decimal places.
If there is no solution, enter NO SOLUTION.)
α = 47.16°, a =
5.04, b = 6.17
smaller c:
c =
β =
°
γ =
larger c:
c =
β =
°
γ =
Solve each question and enter on your correct answers in the
spaces provided at the Test and Quizzes Section on the Sakai LMS
platform. PROVIDE the rough work of your solutions by handwriting,
scanning, converting it into pdf and uploading at the ASSIGNMENT
SECTION of your Sakai. The file must be named with your Student’s
Index Number.
1. If the ratio of the ages of Kissi and Esinam is 3:5 and
that of Esinam and Lariba is 3:5 and the...