Given:
There are given that the cos function:
Explanation:
To find the value, first, we need to use the half-angle formula:
So,
From the half-angle formula:
Then,
Since 105 degrees is the 2nd quadrant so cosine is negative
Then,
By the formula:
Then,
Put the value of cos210 degrees into the above function:
So,
Final answer:
Hence, the value of the cos(105) is shown below:
Answer:
the correct options are:
(–1, 3), (–2, 2) and (–5, –1)
Step-by-step explanation:
Given that a line passes through two points
A(-2, -4) and B(4, 2)
Another point P(0, 4)
To find:
Which points lie on the line that passes through P and is parallel to line AB ?
Solution:
First of all, let us the find the equation of the line which is parallel to AB and passes through point P.
Parallel lines have the same slope.
Slope of a line is given as:
Now, using slope intercept form () of a line, we can write the equation of line parallel to AB:
Now, putting the point P(0,4) to find c:
So, the equation is
So, the coordinates given in the options which have value of y coordinate equal to 4 greater than x coordinate will be true.
So, the correct options are:
(–1, 3), (–2, 2) and (–5, –1)
Answer:
4. Z ≈ 46.1°
5. T ≈ 45.2°
6. F ≈ 15.0°
Step-by-step explanation:
4.
We need to use the Law of Sines, which states that for a triangle with legnths a, b, and c and angles A, B, and C:
Here, we can say that ZY = a = 30, X = A = 110, XY = b = 23, and Z = B. Plug these in to find Z:
Solve for Z:
Z ≈ 46.1°
5.
Use the Law of Sines as above.
Solve for T:
T ≈ 45.2°
6.
Again, use the Law of Sines as before.
Solve for F:
F ≈ 15.0°