Without aid of tables/caulculator, find all values of A between 0 degrres and 360 degrees.
cosec A= sec A
How you do this question?
1/sinA = sin A
sin^2 A = 1
only when sin A = 1 or -1
That is when A = 90 or 270 degrees
sec A is cos A
oops 1 over cos A
Sorry, misread question
1/sin A = 1/cos A
sin A = cos A
45 degrees from x axis in all quadrants the sin and cos have the same magnitude but for this they must also have the same sign. That is in quadrants 1 and 3
45 degrees
180+45 = 225 degrees
To solve the equation cosec A = sec A without the use of tables or a calculator, we need to recall the definitions of cosecant and secant functions.
The cosecant of an angle A (cosec A) is the reciprocal of the sine of that angle, while the secant of an angle A (sec A) is the reciprocal of the cosine of that angle.
So, we can rewrite the equation as:
1/sin A = 1/cos A
To simplify further, we can cross-multiply:
cos A = sin A
Next, we can square both sides of the equation:
cos^2 A = sin^2 A
Using the Pythagorean identity (sin^2 A + cos^2 A = 1), we can substitute cos^2 A with (1 - sin^2 A):
1 - sin^2 A = sin^2 A
Rearranging the terms, we have:
2sin^2 A = 1
Dividing both sides by 2:
sin^2 A = 1/2
To find the values of A that satisfy this equation, we take the square root of both sides:
sin A = ±√(1/2)
Now, we need to determine which angles have a sine equal to ±√(1/2).
The standard angles whose sines are ±√(1/2) are 45 degrees and 135 degrees in the first and second quadrant, respectively.
However, we are looking for all the values of A between 0 degrees and 360 degrees. So, we need to consider the corresponding angles in the third and fourth quadrants, which will be 225 degrees and 315 degrees, respectively.
Therefore, the values of A that satisfy the given equation between 0 degrees and 360 degrees are 45 degrees, 135 degrees, 225 degrees, and 315 degrees.