Answer:
θ = 0.896 and 2.246.
Step-by-step explanation:
We will use the identity
sin²θ + cos²θ = 1
and the double angle formula
cos2θ = cos²θ - sin²θ = (1 - sin²θ) - sin²θ = 1 - 2sin²θ
1. Convert the equation to a more solvable form.
2. Solve the quadratic
a = 2; b = 1; c = -2
(a) Set up the equation.
(b) Evaluate the roots
3. Solve for θ
(a) The negative root
u = sinθ = -1.281
sinθ cannot be less than -1. No solution.
(b) The positive root
If sin(x) = a, then
x = arcsin(x) + 2πn and
x = π - arcsin(a) + 2πn
(i) Case 1
u = sinθ = 0.7808
θ = arcsin(0.7808) + 2πn
θ = 0.8959 ± 2πn
If n = 0,
θ = 0.8959
(ii) Case 2
θ = π - 0.8959 + 2πn
If n = 0,
θ = π - 0.8959 = 2.246
The solutions are θ = 0.8959 and θ = 2.246
The diagram below shows the graph of f(θ) with its roots at 0.896 and 2.246.
Answer:
Cos A = x/z
Step-by-step explanation:
You need to memorize the definitions of all the trig functions and then these types of problems become easy! OK?
Cos = adjacent side/hypotenuse
Cos A = x/z
(A) I got 10(10)=100 points in remote space.
(B) I also got 10(9)=90 points in remote space
Median means middle. How you solve this is by first putting the numbers in order from least to greatest:
36 41 43 45 46 48 48 51 51 52
Now that it is in order in each "level" take away the smallest and largest number until you get to the middle
36 41 43 45 46 48 48 51 51 52
41 43 45 46 48 48 51 51
43 45 46 48 48 51
45 46 48 48
46 48
Now this is a bit tricky because there isn't one number to signify the exact middle. When you have two numbers left you must take the mean of those two numbers. This means that you add the two numbers left and then divide the answer by 2:
46 + 48 = 94
94 ÷ 2 = 47
Hope this helped!
Answer:
-3x^2
Step-by-step explanation:
3x x -x =-3x^2
