SOLUTION: find the other five functions of acute angle A,given that cscA=4 over 3

Algebra.Com
Question 623876: find the other five functions of acute angle A,given that cscA=4 over 3
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
To better understand how this works, let's draw a diagram:
  1. Draw a right triangle. (It doesn't matter how it looks.)
  2. Choose one of the acute angles in the triangle and label it A.
  3. Since the csc ratio is hypotenuse/opposite and since we want A to have a csc of 4/3, label the hypotenuse of the triangle (opposite the right angle) with a length of 4 and label the length of the side opposite angle A with a length of 3.
To find all five of the other functions, we will need the adjacent side, too. Since we have two of the three sides of the triangle, we can use the Pythagorean Theorem to find it. Let's call the adjacent side "b". Inserting "b" and 4 and 3 into the Pythagorean equation we get:

Solving for b:


(ignoring the negative square root since lengths of the sides of triangles cannot be negative)

Now we can find the other 5 functions, using 4 for the hypotenuse, 3 for the opposite side and for the adjacent side:






We don;t usually leave square roots in denominators so we should rationalize tan and sec:
RELATED QUESTIONS

Find the other five trigonometric functions of the acute angle B, given that... (answered by lwsshak3)
Given that theta is an acute angle and tan theta equals u, find the other trigonometric... (answered by stanbon)
Sketch a triangle that has acute angle θ, and find the other five trigonometric... (answered by stanbon)
Sketch a right triangle corresponding to the trigonometric function of the acute angle... (answered by jsmallt9)
Sketch a right triangle corresponding to the trigonometric function of the acute angle... (answered by Theo)
given that tan of theta= 11/6, find the other five trigonometric functions of... (answered by drk)
Given sin(a)=-{{{1/3}}} in quadrant IV, find the exact values of the other five trig... (answered by pmatei)
One of the acute angles in a right triangle is 60°.Find the other acute... (answered by Alan3354,MathTherapy)
Given that sine theta equals 4/5 and theta is acute, find the value of the remaining 5... (answered by Alan3354,ilana)