sinX = 3/4 X is an acute angle..?

Question

what are the other 5 trigonometric functions of X? (X is theta) What does it matter if it's an acute angle?

cscX = 4/3

Answer 1

Sine is positive in quadrant I and II. Two angle have sine equal to 3/4 (one acute and one obtuse). You can do this problem without ever finding the actual value of x.

The easiest solution is graphical. In the first quadrant starting at the origin, draw a segment of length 4, such that it is the hypoteneuse of a right triangle with vertical leg equal to 3. So you have a right triangle with an angle whose opposite side is 3 and hypoeneuse is 4 (definiton of sine). Now calculate the horizontal leg with Pythagorean Theorem [you should get sqrt(7)].

Now that you have all 3 sides of the right triangle, you can determine the trig function based on their definitions.
For example, cos(x) = sqrt(7)/4 and tan(x) = 3/sqrt(7).

I'll leave the others to you. Hope this helps.

Answer 2

The sine of 90 deg is one

So any sine less than 1, greater than zero, the angle is acute.

The angle that has sine of 3/4 is 48.6 degrees.

For a right triangle:

tan = side opposite / side adjacent
cot = side adjacent / side opposite
sin = side opposite / hypotenuse
csc = hypotenuse / side opposite
cos = side adjacent / hypotenuse
sec = hypotenuse / side adjacent
.