SOLUTION: Sketch a right triangle corresponding to the trigonometric function of the acute angle θ. Use the Pythagorean Theorem to determine the third side and then find the other five

Algebra ->  Trigonometry-basics -> SOLUTION: Sketch a right triangle corresponding to the trigonometric function of the acute angle θ. Use the Pythagorean Theorem to determine the third side and then find the other five       Log On


   

Question 719182: Sketch a right triangle corresponding to the trigonometric function of the acute angle θ. Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of θ.
csc θ = 15
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
  1. Draw a right triangle and pick one of the acute angles to be theta, as instructed in the problem.
  2. Rewrite the 15 in the csc equation as a fraction:
    csc%28theta%29+=+15%2F1.
  3. Since the ratio for csc is hypotenuse over opposite, make the hypotenuse of the triangle be a 15 (the numerator of 15/1) and make the side opposite to theta be a 1 (the denominator of 15/1)
  4. Use the Pythagorean Theorem to find the side which is adjacent to theta. (Hint: It will be a square root.)
  5. Now that you have all three sides, the hypotenuse and the sides which are opposite to and adjacent to theta, you can now set up the ratios for the other five trig functions.
  6. Some of the ratios from the previous step will have the square root from step 4 in the denominator. Rationalize these fractions by multiplying the numerator and denominator of the fraction by the square root.