Trigonometry?

Question

This is actually a correct version to my previous question:
if x is more than 0 and less than 180
then sin x = y, means x has two values
while tan x = y and cos x = y
x only has one value?
is it correct?

Answer 1

Consider the sine function, it reaches it's maximum value at x=90 degrees. So since the function is multivalued then you may deduce that f(x) = sin x is symmetrical about x= 90,
but because of the period of the functions there will be two x values which give the same value for the function in the interval given.
f(x) = tan x has a period of 180 degrees so in the given interval the tan function is one to one meaning every x value is mapped to a unique y value in the given interval.
f(x)= cos x is symmetrical about x=0 which is why cos x=cos (-x)
now it is also apparent that the cosine function is one-to-one on the given interval.
So your conclusion is correct.

Answer 2

Sin x is a strictly increasing function in the range: 0 And,Sin x is a strictly decreasing function in the range: 90 So, the value of sin x rises upto 90 degree.But after that the value falls.Therefore you will get 2 values of y when,y=sin x [range:0 But cos x is a strictly increasing function in the range: 0 Therefore you will get 1 value of y when,y=cos [range:0 So, you are correct.

Answer 3

Sin is plus (+) in 1 st and 2 nd (anticlockwise) 1/4 circles. So X has 2 values (if y is +).
And in 1 st all (sin,cos and tan) are ( + ) while tan and cos are (+) again in 3rd and 4th 1/4 circles. So of course you are correct.

Answer 4

Yes when x is greater than 0 and less than 180 means x lies in the first and second quadrant and in the first quadrant all are positive while in the second quadrant only sin x is positive while cos x and tan x are negative.

Answer 5

if u look at a sine curve, between 0 and 180 then two values of x give one y
cos x has one to one, however between -90 and 90 there are 2 values.
tan has one cos it is odd.

so yes, you're correct

Answer 6

If you're trying to say what I think you're trying to say, the answer is yes. There are two calues of x that will give the same value for sin(x). That's the reason that the 'principle value' for sin is -π/2 ≤ x ≤ π/2


Doug