SOLUTION: FOR THE ACUTE ANGLE sin theta =3/5, FIND: COS theta TAN theta COT theta SEC theta CSC theta (sorry! I do not know how to make a theta symbol!)

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Question 1154334: FOR THE ACUTE ANGLE sin theta =3/5, FIND:
COS theta
TAN theta
COT theta
SEC theta
CSC theta
(sorry! I do not know how to make a theta symbol!)
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.

Since sin(a) = 3%2F5, 


    cos(a) = sqrt%281-sin%5E2%28a%29%29 = sqrt%281-%283%2F5%29%5E2%29 = sqrt%281-9%2F25%29 = sqrt%2816%2F25%29 = 4%2F5.


Notice that since the angle "a" is in QI, cos(a) is positive; so, the sign of the square root is positive.


Next, since you know sin(a) and cos(a), you may calculate all other trigonometric functions  tan(a), cot(a), sec(a) and csc(a)


based on their definitions.


In order for make writing easier,  I replaced  "theta"  by  "a"  everywhere.



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

FOR THE ACUTE ANGLE sin theta =3/5, FIND:
COS theta
TAN theta
COT theta
SEC theta
CSC theta
(sorry! I do not know how to make a theta symbol!)
As theta is ACUTE, the 6 TRIG. functions are in Quadrant 1.

matrix%281%2C5%2C+sin+%28theta%29%2C+%22=%22%2C+3%2F5%2C+%22=%22%2C+O%2FH%29

As one of the legs is 3, and the hypotenuse is 5, it's then obvious that this is a PYTHAGOREAN triple, and so, the other leg (longer) will be 4.  

As such, we can see that 

The other 5 TRIG. functions are: 

Now, make the SUBSTITUTIONS.